"I think it's really important if you're going to have your name on anything, that you're hospitable, you're inclusive, you're open arms to everyone that comes, it's a public facility", she said.
"I was fine until lately when she said so many derogatory things about my community, I'm a gay woman - about the LBGTIQ community. that really went deep in my heart and soul".
King's remarks appeared to catch tournament officials off guard.
Court, who has opted to take a crabbing trip rather than attend the Australian Open tennis tournament that runs January 15-28, part of which will be played at the arena named for her, recently chastised the Australian people for voting overwhelmingly in favor of marriage equality in a mail-in ballot that Parliament then honored by making equality the law of the land.
Margaret Court's controversial views remain a talking point at Melbourne Park but leading players have shied away from suggestions of a boycott at her namesake arena.
King, one of the original professionals in women's tennis and victor of 12 major singles titles in the Open era, said she had regularly met with Court at tournaments in the years since they retired after "we grew up together playing each other".
'I was a proponent of her's, trying to get her to the best possible court, ' King said.
"What I felt out there was a lot worse compared to how actually it was", she said.
"Maybe it's our community, the LGBTIQ community -people might feel differently".
"I personally don't think she should have her name [on the court] anymore".More news: Swiss government rules for lobsters to be 'stunned' before being boiled
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King said Court's attacks on sexually diverse people were the last straw.
Court, now a Christian pastor, has been an outspoken opponent of same-sex marriage. So, that's all the devil - that's what Hitler did and that's what communism did: got the mind of the children. King said at a media conference Friday.
'But we're all God's children, so I probably don't think it's appropriate to have her name'.
"I'll play on whatever court I'm scheduled on", she said.
The British number one said: "I don't agree with what Margaret Court said".
"Our position hasn't changed", he told reporters.
"We have reputable sources review all her press releases and interviews and can not trace these remarks back to Margaret". They are not the views of our organization and not the views of our sport. "There should be no thought of changing the name which is embedded in Australian history forever".
Margaret Court Arena generally hosts five marquee matches per day through the first week of the tournament, and is sold as a separate ticket from the rest of the grounds. Reverend Court labeled any players who refuse to play in the arena as "petty" and "childish".
Court is a regular at the event, but is not attending this year's Australian Open, which starts Monday.