"I think if you were talking about Indigenous people, Jews or any other people, I can't imagine the public would want to have her name on something".
Court is a regular at the event, but is not attending this year's Australian Open, which starts Monday.
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". King said she would welcome Court's attendance.
Australian Open 2018: I would BOYCOTT if bosses made me do this, claims former champ
When Rocket, Rod Laver, got given the arena, I said: "what are you going to do for Margaret?" But in light of Court's deeply homophobic statements about LGBT people and marriage equality, which the country's Parliament passed in December, King said at a press conference for the Australian Open on Friday that Court's name should be removed from the arena, reports the Associated Press.
King, a pioneer for equality and diversity in tennis, said she had initially been a proponent of having Melbourne's Margaret Court Arena named 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".
"I was looking forward to seeing her".
She said: "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". When she talks about the children of transgenders that put me over the edge.
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.
Tournament director Craig Tiley said Court had a standing invitation to the season-opening major and would be welcome in the future.
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.
And she suggested that some players would feel more strongly if another group was targeted by Court. Maybe because of our community, the L.G.B.T.I.Q. community, 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". King was the first high profile tennis player to come out, her sexuality became public as part of a palimony suite in 1981.