As controversy mounted over the name of the arena previous year, the host federation maintained nearly complete silence in the face of calls for the name to be changed because of Court's remarks about LGBTQ people and same-sex marriage, which recently became legal in Australia after receiving overwhelming support in a public referendum.
King is in Melbourne to celebrate the 50th anniversary of her Australian Open victory.
"But you do not name a building after her".
"When you were named after Margaret Court, it seemed like the right thing to do", Navratilova explained in 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".
Court said people should vote no "for the sake of Australia, our children, and our children's children".
'I was a proponent of her's, trying to get her to the best possible court, ' King said. When she talks about the children of transgenders that put me over the edge. "We are all God's children, so I probably don't think it's appropriate to have her name".
And she suggested that some players would feel more strongly if another group was targeted by Court.
"I wish Margaret was here this year", she said.
"That's what Hitler did and that's what communism did, got the minds of the children".
Billie Jean King has called for Australian Open organisers to rename the Margaret Court Arena in Melbourne following the controversial comments made by the former Australian tennis player about homosexuality and transgender people.
- On apartheid in South Africa, she said in 1970: 'It is a tragedy that politics has come into sport. "That really went deep in my heart and soul and I personally don't think she should have her name (attached to the arena) any more".
King was keen for Court to be honoured for her remarkable career by having a stadium named after her, but now thinks the title should be stripped for her "derogatory" comments.
"I have my name on the whole facility in the US [the US Open is played at the Billie Jean King National Tennis Center] and every time I see my name up there I can hardly breathe because of the responsibility".
However, she said comments from her friend a year ago blaming the devil for people being transgender "put her over the edge".
"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", she continued.
"It is now clear exactly who Court is: an unbelievable tennis player, and ... a homophobe".
Organizers have recognized the American tennis great as the Australian Open Woman of the Year and launched its "Open4All" initiative to promote equality, diversity and inclusion to coincide with King's visit.