Margaret Court does not believe Serena Williams has ever "admired" her and claims the modern game is significantly easier than it was in her own era.

Williams, widely considered one of the greatest sportspeople of all time, stepped away from top-level tennis following defeat to Ajla Tomljanovic in the third round of the US Open.

Although her time on tour now looks to be over, the 40-year-old admitted "you never know" when asked about future appearances, but a U-turn is widely considered to be highly improbable.

Williams is bowing out with 23 grand slam singles wins – one fewer than record holder Court.

Court, 80, is a Pentecostal church pastor now and has been criticised in recent years for comments about race, homosexuality and the transgender community.

She was blunt when asked about her feelings on Williams, telling the Telegraph: "Serena, I've admired her as a player. But I don't think she has ever admired me."

Court won her grand slam singles titles between 1960 and 1973, and the Australian believes players in the modern era have it much easier than she did during her remarkable career.

"I would love to have played in this era; I think it's so much easier," she said. "How I would love to have taken family or friends along with me. But I couldn't, I had to go on my own or with the national team.

"People don't see all that. As amateurs, we had to play every week, because we didn't have any money. Now, they can take off whenever they want, fly back whenever they want.

"We would be away for 10 months. That's why I first retired in 1965, because I used to get homesick. You might be with the odd other person, but it's not like having your family there.

"We didn't have psychologists or coaches with us. It's a whole different world. That's what disappoints me; that players today don't honour the past of the game."

Serena Williams will go out with "full force" when she begins her final US Open campaign before retiring, according to Chris Evert.

Williams will have one last chance to match Margaret Court's all-time record of 24 grand slam singles titles at Flushing Meadows, as well as an opportunity to wave goodbye to her adoring fans on home soil.

While a challenge for the trophy looks highly improbable for Williams this time around, fellow six-time US Open winner Evert suspects the 40-year-old will take some shifting from the draw.

According to Evert, "the edge is off" when it comes to Williams and her remaining tennis goals, meaning she has reconciled herself to the likelihood of finishing her career with 23 singles majors.

Williams has revealed family matters and business interests were key to her decision to "evolve away" from the sport, and with her on-court returns diminishing, now seems the time to head in that direction.

Yet Evert can see Williams, who faces Danka Kovinic in round one in New York, giving a good account of herself during her US Open swansong.

"Serena isn't coming out to play her last match; she's coming out with full force," Evert said on ESPN. 

"The way she's been practising this week, she's here to compete, she's here to win, and I don't even think she's thinking about retirement at this stage."

Williams holds a 106-14 win-loss record in singles at the US Open. Her match wins tally at Flushing Meadows is the highest by any woman at the competition in the Open Era, and only Martina Navratilova has more at a single slam, achieving an astonishing 120 victories at Wimbledon.

Williams and Evert lead the way in women's US Open titles in the professional era (since 1968), and regardless of final grand slam tallies, there will always be debate over who ranks as the greatest player of all time.

Williams certainly has a strong case, yet Navratilova (1,442), Evert (1,309) and Steffi Graf (900) all won more WTA-level matches than Williams (856), who often played a limited schedule.

Court has the most grand slam titles on the women's all-time list, with a remarkable haul of 64 when women's doubles and mixed doubles are included. Navratilova is next with 59, before Williams and Billie Jean King sit joint third with 39 majors apiece.

Scheduling self-preservation has allowed Williams to play on for so long, and John McEnroe has raised the question of what might happen if his fellow American surprises herself by clinching a seventh Flushing Meadows triumph. 

"If she did happen to win this, don't you think it'd be tempting to go and break the record?" McEnroe asked.

Four-time US Open singles champion McEnroe added: "I think she's accepting, as much as Serena Williams can, that she's not going to win this.

"Maybe deep down she's found some sort of belief that maybe somehow, if she gets the right set of situations going, she can make a real run."

More realistic, in McEnroe's mind, is the prospect of Williams and sister Venus having a deep run in the doubles after they were handed a wildcard.

As a partnership, the siblings have won 14 grand slam doubles titles, never losing in a final at the majors.

"The two of them in doubles, where they're covering half the court and they're still able to do their thing, that would be a hell of a way to go out," McEnroe said.

Martina Navratilova said she was "gutted" to miss Wimbledon's Centre Court centenary celebration after testing positive for COVID-19 on Sunday.

The nine-time champion was absent from a parade of champions, and in a series of posts on social media she explained why she had to sit it out.

Past winners were introduced to the main show court's middle Sunday crowd, with the one-time champions going first, all the way through to eight-time Wimbledon king Roger Federer.

Navratilova would have come out last of all, as the most successful singles player in Wimbledon history, but she was unable to take part. Including doubles, Navratilova won 20 slam titles at Wimbledon.

"Unfortunately I will miss it as I just tested positive this morning," she wrote on Twitter shortly before the ceremony. "Am so bummed!!!! I am gutted I can't be there."

Confirming she had the coronavirus, Navratilova wrote: "Yup, got it here for sure… oh well. So wanted to be on that court with so many champions of our sport."

Asked how she was feeling, the 65-year-old Czech-born American added: "Not too bad so far- wouldn't want to play tennis but ok… fingers crossed."

A host of greats of the game delighted the crowd, with stars of the women's tour including Navratilova's former great rivals Chris Evert and Billie Jean King, along with Margaret Court and Venus Williams, while Federer was joined by a field of fellow men's superstars that included Rod Laver, Novak Djokovic, Stefan Edberg, Rafael Nadal and Andy Murray.

Three-time former champion Boris Becker was another notable absentee, after the German was jailed in April for offences relating to his 2017 bankruptcy. Seven-time winner Serena Williams also missed the event, after her first-round defeat.

Navratilova has been working at Wimbledon during the championships, notably appearing as a member of the BBC broadcast team.