Court (picture above), 75, who holds the record for most Grand Slam singles titles across the amateur and Open eras, is now a Christian pastor who lives in Perth, Western Australia and has campaigned against the introduction of gay marriage..
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.
"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 news conference on Friday. "That really went deep in my heart and soul.
"I personally don't think she should have (her name on the stadium) anymore."
King is attending the Australian Open for the first time in eight years, marking the 50th anniversary of her Australian title.
She said if she was still competing, she would not play at the Margaret Court Arena.
Organisers have named the American tennis veteran 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.
King, one of the original professionals in women's tennis and winner of 12 major singles titles in the Open era, said she had regularly met Court at tournaments in the years since they retired after "we grew up together playing each other".
Court's comments before Australia voted in favour of legalising same-sex marriage were heavily criticised last year, with 18-time Grand Slam singles winner Martina Navratilova writing an open letter condemning the remarks and urging officials to rename the arena at Melbourne Park.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
