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 He's an inconsistent player, who is very withdrawn," Sagnol told French radio station RMC.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.
The defender has been strongly linked in recent days with a switch to OL, who next season will be aiming to atone for a disappointing 2019-20 campaign.
Sakho, 30, joined Palace in 2017 after spells at Liverpool and Paris Saint-Germain and has won 29 caps for France, albeit just two since 2015.
Injuries have impeded Sakho this season and he has made just six Premier League starts for Palace during the disrupted campaign, which has been suspended since March due to the coronavirus pandemic.
That appearance record is what worries ex-Bayern Munich defender Sagnol, who is concerned Lyon may face a hefty price tag for a player with a track record for missing a large number of games.
Sagnol, France's 2006 World Cup right-back, told French broadcaster RMC's After Foot show: "When an English club allows a player who is just 30 to leave, it's not a good sign.
"The Premier League demands a lot physically, athletically and in terms of intensity. It's a league that wears you out.
"In terms of character, yes, I think he can bring a lot to this team. The lack of character has been a recurrent evil at Lyon for three or four years. But he can only bring that if he isn't injured regularly."
Sagnol admitted he had not seen Palace or Sakho in recent action, adding: "But I think if he had been in good form, we would have seen him back in the France team.
"We haven't seen him back and that's not very positive. For me, when we have a big transfer in terms of price and salary, you have to reduce the risks of a mistake for French clubs. With this, I think there are a lot of risks."
