Andy Murray voiced his support for gay marriage in the wake of controversial comments from Margaret Court but believes any player action should come before next year's Australian Open rather than during it.
It comes after a first-round French Open win for the Scot over Andrey Kuznetsov, beating the Russian 6-4 4-6 6-2 6-0.
Australian women's number one Sam Stosur hinted on Monday that players could refuse to compete on Margaret Court Arena, one of Melbourne Park's prime show courts, at next January's tournament.
Court, a 24-time grand slam singles champion turned Christian pastor, has long voiced her opposition to gay marriage.
She sparked more controversy last week after saying she would boycott the Australian airline Qantas because of chief executive Alan Joyce's support for same-sex union.
That led to condemnation from within tennis and calls to change the name of the stadium at Melbourne Park, with Martina Navratilova one of those to voice her support.
Following his first-round win over Andrey Kuznetsov at the French Open, Murray said: "I don't see why anyone has a problem with two people who love each other getting married.
"If it's two men, two women, that's great. I don't see why it should matter. It's not anyone else's business. Everyone, in my opinion, should have the same rights. I don't agree with that (Court's stance)."
Asked if he would support a potential boycott, Murray said: "If something was to be done, I think it would be a lot more beneficial to do it before the tournament starts.
"For players to be in a position where you're in a slam and boycotting playing on the court, I think would potentially cause a lot of issues.
"So I think if something was going to be happen and the players come to an agreement, if they think the name should be changed or whatever, that should be decided before the event starts.
"But I would imagine a lot of the players would be pretty offended. So we'll see what happens."
Stosur is not expecting the name to be changed but does not feel players should sit back and do nothing.
She said: "I find it very hard to believe that it would ever be changed, but the court's named Margaret Court Arena because of what she did in tennis.
"I think everyone can have their opinion. I don't agree with it, but I guess we'll cross that bridge when we all get down to the Australian Open next year and who wants to play on Margaret Court Arena and who doesn't."
Stosur's fellow Australian player Casey Dellacqua has been the loudest voice in opposition to Court.
She tweeted a message saying, "Margaret. Enough is enough" last week accompanied by a newspaper article with quotes from Court criticising Dellacqua's family arrangements.
Dellacqua has two children with partner Amanda Judd.
Stosur added: "It's been pretty fiery. Casey was obviously very adamant, and I wanted to support my friend and that's why I sent out my first tweet in a very long time."
Tennis Australia issued a statement in response to Court's comments.
It read: "As a legend of the sport we respect Margaret Court's achievements in tennis and her unmatched playing record.
"Her personal views are her own, and do not align with Tennis Australia's values of equality, inclusion and diversity."