Court's non-appearance at the Open - which overlaps Melbourne's annual queer festival Midsumma - is likely to lessen the likelihood of demonstrations.
American tennis legend Billie Jean King has called for the Margaret Court Arena at the to have its name changed due to the former great's outspoken views on gay issues.
"I'm a gay woman".
When the arena was named after Court in 2003, King supported it.
'I was fine until lately when she said so many derogatory things about my community - I'm a gay woman - and that really went deep in my heart and soul.
"I think it's its really important, if you're going to have your name on anything, that you're hospitable, inclusive, you're opening arms to everyone that comes to a public facility", she said.
Meanwhile, King, who just this week attended the Golden Globe Awards for the film Battle of the Sexes, about her famed match with self-professed male chauvinist pig Bobby Riggs, is attending the Australian Open for the first time in eight years.
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Court remains the all-time leader for Grand Slam titles in the women's game with 24 wins, one clear of Serena Williams.
King said she wouldn't promote a boycott of the stadium, but encouraged players to "look inside their heart" before making a decision.
"I think there will be a price to pay for it in the future in the nation and people will see it's not about marriage", Court said after the marriage vote.
The rebranding of a show court as "Margaret Court Arena" has brought to attention the West Australian fundamentalist's Christian views on same-sex parenting, and LGBTI rights.
Court's negative comments about gay people before Australia voted in favor of legalizing same-sex marriage were heavily criticized a year ago.
Court has repeatedly criticised "the gay lobby" for trying to influence children with the Safe Schools program, which aims at promoting the acceptance of LGBTQ+ students.
After Navratilova's letter, Tennis Australia (TA) released a statement saying Court was unmatched as a player, but her personal views were out of line with TA's "values of equality, inclusion and diversity".
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If they keep him for the season, they could receive a compensatory pick after he turns down a qualifying offer. Otherwise they might have to deal with a potentially losable grievance - and still have to pay the salary.
The British number one said: "I don't agree with what Margaret Court said".
Court is not attending this year's Australian Open, which starts Monday, but has been a regular guest in the past.
Australian Open tournament director Craig Tiley said Tennis Australia didn't have a view on the renaming of the arena.
He said there had been "conversation" among stakeholders of Melbourne Park regarding the issue, but there was no process in place to change the name of the stadium.
Unfortunately, the arena can not be named after King as the facility that hosts the United States Open in Flushing Meadows, N.Y., was christened the Billie Jean King National Tennis Center in 2006.
King said she would welcome Court's attendance.
"You can have discussion around it".
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King said she would refuse to play on the arena if she was appearing at this year's tournament. "It's a public facility".