"I don't think she should have her name (on it) any more".
Court will not attend this year's event, and has opted to go on holiday instead in her native Western Australia, where she is a pastor at the Victory Life Centre, a church with deeply conservative views on social issues.
Court pictured during her victorious 1970 Wimbledon singles final against Billie Jean King.
The former 64-time major victor, who is now a pastor at Victory Life Church in Perth, also once wrote a letter to the West Australian to express sadness that Casey Dellacqua's newborn child would be "deprived of his father".
When Rocket, Rod Laver, got given the arena, I said: "what are you going to do for Margaret?"
King said if she was still competing, she wouldn't play on Margaret Court Arena.
King, a trailblazer for equality and diversity in tennis, said she had initially been a proponent of having Margaret Court Arena named in 2003 in recognition of the 24-time Grand Slam singles winner's contribution to the sport.
King, who is an open lesbian, added that Court's homophobia had "really went deep in my heart and soul".More news: 'Are you a racist?' Donald Trump questioned over 's***hole' remarks
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"Mrs Court's ongoing claims that tennis has been infiltrated by lesbians and that older female players have corrupted younger female players are homophobic at the very least and paint same-sex attracted people as predatory opportunists". "I personally don't think she should have her name (on it) any more", King, 74, told reporters at Melbourne Park.
"I'll play on whatever court I'm scheduled on", she said.
King is attending the Australian Open for the first time in eight years, marking the 50th anniversary of her Australian title.
"I was fine until lately when she said so many derogatory things about my community-I'm a gay woman-about the LBGTIQ community", King said at a news conference.
"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.
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 refuse to play on the arena if she was appearing at next week's tournament, but she wouldn't counsel others to do so. "I wouldn't encourage them not to do it", she said.
'Maybe it's our community, the LGBTIQ community (why) people might feel differently.
- Slammed Australian doubles player Casey Dellacqua after her partner, Amanda Judd, had given birth to a son, claiming the child's birth hinted at the threat of a "fatherless generation".