"I just feel like she's gotten really derogatory. It's a public facility". "That really went deep in my heart and soul", King told a news conference in Melbourne on Friday.
"I was fine until lately when she said so many derogatory things about my community; I'm a gay woman", King added.
Another gay tennis champion, Martina Navratilova has recently said that she would not play at the Margaret Court Arena if she was still playing professionally.
Australian Open tournament director Craig Tiley was quoted as suggesting that "conversations" had been held about the court's name, but stopped short of indicating that a change was in the offing.
"They're about equality, they're about showcasing men and women, wheelchair tennis; celebrating tennis in that way".
The tennis champion admits that she was one of the proponents of the push to have part of the Rod Laver Arena named after Court in recognition of her tennis achievements, but says Court's comments about gender and sexuality have gone too far. Maybe because of our community, the L.G.B.T.I.Q. community, people might feel differently. But we're all God's children.
'I don't think she should have her name (on it) any more'.
Court also criticised Australian player Casey Dellacqua for having two children with her female partner, and her comments led to a threat of a boycott at the third show court in Melbourne that was named after the 24-grand slam victor in 2003.
"That's all the devil - that's what Hitler did and that's what communism did: got the mind of the children", Court said on 20 Twenty Vision Christian Radio.
King said there was no coming back from those remarks. In another interview she said transgender children were "the devil". "We are all God's children, so I probably don't think it's appropriate to have her name".
The 74-year-old American, who won 12 major singles titles, she had originally backed Court to be honoured by the naming of the stadium, but the Australian's outspoken views in recent years had changed her mind. I was looking forward to seeing her.
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".
The players have been placed in a hard position and Konta was one of the few willing to really engage with the subject at her pre-tournament press conference.
"Margaret's views are her views, they're not the views of our organisation, they're not the views of our sport".
In sport, nearly always a bastion of conservatism, those holding disreputable views have long adorned not only stadia, but also the administration of games. We're inclusive, diverse, equal, and all the things Billie Jean said.
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.