The former Schalke player is coming towards the end of his fourth year at Manchester City.
He looked set for a switch to Bayern last year before suffering a major knee ligament injury in the Community Shield against Liverpool in August.
Having battled his way back to fitness, Bayern are again looking set for an attempt to land the 24-year-old.
Former Bayern defender Willy Sagnol says his old club would be better off chasing Bayer Leverkusen's 20-year-old rising star Kai Havertz, however, claiming Sane simply does not fit the bill.
"He doesn't match up at all to Bayern, in terms of character. He's an inconsistent player, who is very withdrawn," Sagnol told French radio station RMC.
"For me, he isn't made for this club.
"He's got lots of problems, at Manchester City and with the national team. We've said that he'd cost €80million. At a pinch, I'd prefer to put down €20m more and buy Havertz to be happy.
"With Havertz, it's the guarantee of a playmaker that you could play with Lewandowski without a problem. [Thomas] Muller won't last forever."
Former Bayern president Uli Hoeness said on Saturday he hoped the club could sign Havertz as well as Sane, but he cast doubt on whether financial realities would allow for that.
Thomas Tuchel's side took a deserved lead into half-time thanks to a fine finish from Kai Havertz, who had scored the winner in the Champions League final in May.
Havertz clipped a clever shot high beyond Bernd Leno after being played into space by Timo Werner, who missed a good chance for a second three minutes later.
The Gunners, who brought on new signing Ben White at half-time, drew level 69 minutes in when Granit Xhaka headed in Nicolas Pepe's cross.
However, Chelsea's lead was restored within four minutes as Tammy Abraham slotted a precise finish beneath Leno following a mistake by Hector Bellerin.
Arsenal should have been given an equaliser when Joe Willock crashed a shot off the crossbar and the ball appeared to bounce over the line, but with goal-line technology not in use, it was not awarded.
Mikel Arteta will also be concerned to see midfielder Thomas Partey forced to go off with what appeared to be an ankle injury in the first half.
Chelsea will now face Tottenham on Wednesday before Arsenal take on their north London neighbours on August 8.
Havertz continued to burnish his reputation with a first-half brace as Leverkusen crushed lowly Werder Bremen 4-1 in the Bundesliga on Monday.
The Germany international – frequently the topic of transfer gossip columns amid links to Liverpool, Manchester United and Arsenal – opened the scoring in the 28th minute and restored Leverkusen's lead five minutes later following Theodor Gebre Selassie's equaliser.
After thrashing relegation-threatened Bremen behind closed doors at Weser-Stadion due to the coronavirus pandemic, Bosz told reporters: "Kai [Havertz] is a special player, but I don't think he made his best game today. He can do much better.
"I've known him for a long time now and I know he can do much better. It has to do with the rhythm. But for every player the captain's armband is something special. And so it will be for Kai."
Havertz, 20, added: "I'm very happy. We didn't make many mistakes and deservedly won.
"Now we want to continue like this on Saturday in Monchengladbach."
The result was Leverkusen's fourth in succession as the Bundesliga returned over the weekend following the COVID-19 outbreak.
Leverkusen are fifth in the table, eight points behind defending champions and leaders Bayern Munich.
"We are naturally satisfied, as you have to be when you win the first game after a two-month break with 4-1 in Bremen," Bosz said. "There were many question marks before. I think we deserved to win, although we didn't always play very well. That has to do with the rhythm.
"We lost easy balls during the game, which we normally don't lose. But like I said, if you win 4-1 here, you have to be satisfied. And I am satisfied."
Thiago is contracted until the end of 2020-21 but the Spain international is reportedly on the verge of leaving for Premier League champions Liverpool as Bayern brace for his exit.
The 29-year-old came off the bench with three minutes remaining in Bayern's 4-2 victory over Bayer Leverkusen in Saturday's DFB-Pokal final.
However, Flick has not given up on keeping star Thiago – who arrived from Barcelona in 2013 and has since won seven successive Bundesliga crowns among other honours.
"The thing is, I always have hope. I'm actually always very positive about things," Flick told reporters following the Berlin triumph.
"I also know, of course, that when you're at a certain age and you've already played in the Spanish league with Barcelona and in the Bundesliga with Bayern Munich, you feel the need to experience another big league. That is quite normal and that is also human.
"I'm trying my best to make sure Thiago stays here and that you can convince him to stay. But that's one thing that time will show.
"We still have the Champions League ahead of us now and we have a lot of plans, also together with him."
Flick was also asked about Bayern's transfer plans after prising Germany international Leroy Sane from Manchester City.
Bayern have been linked to Leverkusen star Kai Havertz, who scored a late consolidation goal on Saturday.
"We all know that of course the time with coronavirus has changed a lot," Flick added. "This means that many clubs, including FC Bayern Munich, can no longer spend money so easily. That's why we have to proceed cautiously.
"For now, Leroy Sane's commitment was important for the club and also for the team, which are taking the next step. Hasan Salihamidzic did a very good job of staying on the ball. I think a lot is developing and we have to see that we are a bit more broadly based."
Leverkusen were the superior side in a generally low-key contest, playing some eye-catching football on occasions as they bounced back from a shock 4-1 defeat to Wolfsburg on Tuesday.
They were fortunate to be on level terms at half-time, as Roland Sallai fed Lucas Holer in behind Sven Bender, but the forward failed to hit the target when one-on-one with Lukas Hradecky.
The visitors capitalised early in the second half. Leon Bailey, who had been a source of frustration, twisted and turned his way into the Freiburg penalty area and played a reverse pass to Havertz, who somehow poked his effort through the legs of Alexander Schwolow from an acute angle.
Havertz trudged off just past the hour after picking up what appeared to be a minor knock, but Leverkusen held on for a slender win – Hradecky making sure of the victory late on when turning a Nils Petersen effort around the post.
Leverkusen moved a point clear of RB Leipzig, who, along with Borussia Monchengladbach, can usurp Peter Bosz's side again when they face Cologne and Union Berlin respectively.
Germany allowed Havertz to leave their training camp in Stuttgart on Friday to complete a switch to Chelsea, where he signed a five-year contract.
The Blues also raided the Bundesliga for RB Leipzig striker Timo Werner, with Hakim Ziyech, Ben Chilwell, Thiago Silva and Malang Sarr having also arrived at Stamford Bridge as reinforcements for the 2020-21 season.
Low was disappointed to see Havertz leave the Bundesliga but hopes playing abroad can help him have a bigger impact with the national team.
"I see it as a negative when such great talents like Kai are no longer in the Bundesliga," Low told a news conference on Saturday.
"But I also see the positives. Abroad, the players develop their personalities.
"I think the time is right for Kai, and the same goes for Werner. If they take the next step that will of course help us too."
Havertz was an unused substitute in Germany's 1-1 draw with Spain in the Nations League on Thursday, with Low not playing him due to his Chelsea transfer not being completed at that point.
"Kai was torn. Kai would have been good for us in the second half against Spain, but I also knew his situation," said Low.
"He would have liked to have played for the national team, but in such situations, when a transfer is imminent, you have to be careful."
Germany will be without Havertz when they face Switzerland on Sunday but Low expects to have every other player available, having confirmed Leroy Sane did not suffer a muscle injury against Spain.
"Bernd Leno will be in goal. For everyone else, I'll wait for training," said Low.
"I told Leroy we weren't taking any risks. He did not suffer any muscular injuries, but it was not to be expected that he would last the 90 minutes.
"Switzerland's development has been very good since 2014, including as individuals. They are now one of the big players. I see parallels between Switzerland and Spain in terms of the style of play."
Germany led 2-0 after a 52nd minute penalty from Ilkay Gundogan and a goal from Kai Havertz in the 67th, but that advantage was wiped out in just over 15 minutes.
Luke Shaw struck in the 72nd, Mason Mount equalised three minutes later, and a penalty to Harry Kane put the English up 3-2 in the 83rd.
Ultimately, an 87th-minute leveller from Havertz saw the two sides share the points, and it gave Flick some mixed emotions.
"The first half was balanced, in the second we deservedly led 2-0 – then we made individual mistakes," he said. "It must not happen that we give up a lead like that.
"But we came back, that's the positive. It was a good test, we take a lot of positive things with us, but also negative things. There's some work for us to do, but we're optimistic, otherwise we could stay at home."
Midfielder Joshua Kimmich provided a little more insight into exactly what went wrong to allow such a rapid collapse.
"We had everything under control and deservedly led 2-0 – then we became far too passive," he said. "No longer pushing through consistently, defending far too deep, no longer having the courage to play against the ball… but in terms of body language and engagement, it was an improvement.
"Everyone now has six weeks to get a good feeling and then we will attack."
After scoring two goals, Havertz said to only get a draw from a match like that "must of course worry you" but suggested that it "was another good game to learn from".
Meanwhile, Gundogan was not afraid to talk about Germany's lofty goals, saying they are heading to Qatar with the plan of making the final.
"It's not unrealistic," he said. "Of course, a lot has to come together. I don't see a team that is miles ahead.
"We have shown over long periods that we can do it at the highest level. We have to try to do that for 90 minutes. At a World Cup you have much less leeway to make mistakes than today."
Havertz scored the winning goal as Leverkusen moved up to third in the Bundesliga by edging Freiburg 1-0 away from home.
The in-demand Germany international, who made it five goals in four games since the coronavirus-enforced break ended this month, hobbled off just past the hour with a knock but Bosz allayed the injury concerns.
"He is fine. I don't know how bad it is, but I think he's gonna be okay," Bosz said after the match.
It was a record-breaking outing for Havertz, who has been linked with the likes of Real Madrid, Liverpool, Bayern Munich and Manchester United.
The 20-year-old midfielder scored his 35th Bundesliga goal, making him the first player under the age of 21 to reach that total.
"I'm very happy for him, of course," Leverkusen team-mate Leon Bailey told bundesliga.com. "He's very, very talented - I think we all know that."
"For him to be able to be doing that gives young players a vision," Bailey added. "Anything is possible once you work hard. I think Kai Havertz is a very hardworking player.
"He's smart, and very intelligent on the pitch. I hope he continues to do this and help the team as much as possible because we need him."
Sancho, who left Manchester City for Borussia Dortmund in 2017, has been heavily linked to Manchester United, as well as Chelsea, Liverpool and Real Madrid.
Dortmund are reportedly preparing for life without the England star.
TOP STORY – BVB BRACED FOR SANCHO DEPARTURE
Borussia Dortmund believe Jadon Sancho's exit at the end of the season is inevitable, according to The Evening Standard.
Dortmund star Sancho has been tipped to join Manchester United, who are determined to boost their attacking stocks.
Chelsea, Liverpool and Real Madrid have also been linked as Bundesliga outfit Dortmund hold out for €129million (£116m).
Dortmund are also running out of patience with Sancho's off-field issues, after the England international was fined for flouting social-distancing guidelines following a haircut.
ROUND-UP
- Juventus could raid Italian rivals Roma for Italy star Nicolo Zaniolo. Calciomercato says Roma could be forced to sell their best players due to the club's financial situation, giving Juve the chance to bring the 20-year-old to Turin.
- Mundo Deportivo claims Inter want €80m for Madrid target Milan Skriniar. The Inter defender is seen as a replacement for veteran Los Blancos captain Sergio Ramos.
- United and Inter are battling to sign Bayern Munich midfielder Corentin Tolisso, reports RMC Sport. The Frenchman moved to Munich from Lyon in 2017.
- Madrid are ready to join the chase for Bayer Leverkusen star Kai Havertz, according to The Sun. The Germany international is wanted by United, Liverpool and Chelsea and the Premier League reportedly appeals to the 20-year-old.
- Ligue 1 holders Paris Saint-Germain are interested in Gianluigi Donnarumma, however, Tuttosport says Serie A champions Juventus are eyeing a move for the Milan and Italy goalkeeper.
- Sky Sport Italia claims Roma are trying to lock down Lorenzo Pellegrini to a new contract amid interest from Inter, PSGand Dortmund.
- Madrid'spath to Rennes sensation Eduardo Camavinga could become complicated. With the Ligue 1 transfer window already open, RMC Sport suggests PSGcould try to trump Madrid for the 17-year-old.
- Sport reports Barcelona are willing to lower their asking price to accelerate Philippe Coutinho'sdeparture. The out-of-favour Brazilian has been linked to Tottenham, Newcastle United and Chelsea.
Chelsea recorded a 2-0 win over Wolves on Sunday to secure a top-four finish in the Premier League and a spot in next season's Champions League.
That result should open the door for the arrival of Havertz – and soon.
TOP STORY – HAVERTZ TO CHELSEA SET TO SPEED UP
Chelsea's qualification for the Champions League should see a deal for Leverkusen star Havertz speed up, according to Sport Bild.
Leverkusen are in the Europa League last 16, but reportedly do not insist on keeping the Germany international for the rest of the tournament.
Havertz, 21, has scored 17 goals and provided nine assists in 43 games in all competitions this season.
ROUND-UP
- Coming out of contract at Milan, Ibrahimovic could be set to extend his stay. CalcioMercato reports the 38-year-old forward is open to accepting a deal worth around €4million, lower than his initial demand of €6m. The report also says Gianluigi Donnarumma, whose deal expires next year, could renew until 2023.
- What's next for Philippe Coutinho? The cover of Sport says the playmaker, who is on loan at Bayern Munich from Barcelona, is considering options to join Arsenal, Tottenham or Leicester City.
- Brescia star Sandro Tonali is linked with a big-money move. CalcioMercato says Inter have agreed terms with the Italy international midfielder and are nearing a €35m agreement with Brescia, while Milan are also reportedly interested in the 20-year-old.
- With Dejan Lovren reportedly set for an exit, Liverpool may have found a replacement. Sport Bild reports the Premier League champions have started talks with Schalke to sign 20-year-old centre-back Ozan Kabak.
- With uncertainty over Kepa Arrizabalaga's future at Chelsea, the Premier League club are said to be looking for a new goalkeeper. Voetbal International reports Chelsea and Leverkusen have strong interest in Ajax goalkeeper Andre Onana.
- Edinson Cavani may be close to deciding his future. Todofichajes reports the former Paris Saint-Germain striker is close to agreeing a deal with Benfica.
However, prising Sancho away from Borussia Dortmund is proving difficult.
United, as a result, could be about to walk away.
TOP STORY – UNITED SET TO GIVE UP ON SANCHO
Manchester United are ready to abandon their pursuit of Borussia Dortmund star Jadon Sancho, according to the Mirror.
United have been unable to agree a fee with Dortmund for England sensation Sancho, who is valued at €120million (£108m).
Now, United are willing to give up on Sancho until next year, which could see the likes of Real Madrid, Barcelona and Liverpool enter the fray.
ROUND-UP
- Marca claims Barcelonahave re-opened talks with Inter regarding star forward Lautaro Martinez. As Barca look to move on veteran Luis Suarez, the embattled LaLiga giants remain keen on Inter's Martinez, despite links to Lyon star Memphis Depay.
- Arsenal have joined Premier League rivals Liverpool in the race to sign Bayern Munich midfielder Thiago Alcantara, reports the Daily Mail. Thiago is eyeing a switch to Liverpool, though the English champions are believed to be unwilling to meet Bayern's demands.
- According to the Mirror, Barca have been quoted £143m (€158.6m) to sign Richarlison from Everton.
- Tuttosport claims former Juventus head coach Massimiliano Allegriis preparing to replace Antonio Conte at Inter. Conte is reportedly set to leave San Siro following one season at the helm.
- Arsenal have agreed a deal to sign Lille defender Gabriel Magalhaes, says Fabrizio Romano. Also linked to Napoli, Everton and United, Gabriel will fly to London on Monday to sign a contract until June 2025.
- Romano also claims Chelseawill announce the signing of Leicester City full-back Ben Chilwell in the coming days as the Blues also target Paris Saint-Germain veteran Thiago Silva and continue negotiations with Bayer Leverkusen for Kai Havertz.
- Leicester are considering Ajax left-back Nicolas Tagliafico as a replacement for Chelsea-bound Chilwell, says the Daily Mail.
- Roma star Edin Dzeko only wants to leave the capital club for Juve, reports Tuttosport. Cristiano Ronaldo reportedly sees Dzeko as the perfect strike partner under Andrea Pirlo.
- As new boss Ronald Koeman oversees a Barca rebuild, Sport reports Ajax would demand €55m for Donny van de Beek. The Netherlands international has also been linked to Madrid and United.
- Monaco coach Niko Kovac wants the Ligue 1 side to sign former Dortmund midfielder Mario Gotze, according to Le10 Sport. Gotze is a free agent after leaving Dortmund.
Bayern were rumoured to be in the running for the Germany international, but it has been reported that Chelsea have triggered his £54million (€60m) release clause.
Werner has played a direct part in 32 Bundesliga goals this term - second only to Borussia Dortmund star Jadon Sancho - and Flick acknowledges the Premier League side have pulled off a big signing.
"He is a very good player, a player who scores goals," Flick said at his pre-match news conference ahead of Saturday's league clash with Bayer Leverkusen.
"This is Timo's decision and you have to respect it. If what's being reported is true, then Chelsea have made a very good signing."
As well as being linked with Werner, Bayern have also been tipped to sign one of Leroy Sane or Kai Havertz when the transfer window opens.
Havertz last week became the first player in Bundesliga history to reach 35 goals before the age of 21 with his strike against Freiburg, and Flick admits he would like to have the "exceptional" forward at Bayern.
"I think there aren't too many coaches who would mind having Kai Havertz in their team. Me included," he said ahead of Bayern's trip to BayArena.
"I've known Kai for a long time, since I accompanied Germany during the Under-17s European Championship in Azerbaijan. Even then he showed how good of a player he was.
"There were two or three really good players and he is the one who developed the most since then for sure.
"Kai is player who moves between the lines very intelligently and has got a good speed. He is very calm with the ball and we saw that against Freiburg.
"He's got that goal instinct and is able to put the ball through the smallest gaps at his young age. This is exceptional. Obviously it's nice to have players in your team who score."
