John McEnroe has called on Serena Williams to overtake Margaret Court's record of 24 Grand Slams and "leave her offensive views in the past".
On Monday, the Australian Open held a ceremony to mark 50 years since Court completed a calendar Grand Slam.
But the 77-year-old Australian has been criticised for her views on gay marriage and transgender athletes.
McEnroe says Court, who has one more major singles title than Williams, is a "nightmare" for Tennis Australia.
In a video for Eurosport, the seven-time Grand Slam champion said: "There's only one thing longer than the list of Margaret Court's list of achievements: it's her list of offensive and homophobic statements.
"Serena, do me a favour, get two more Grand Slams this year and get to 25 so we can leave Margaret Court and her offensive views in the past, where they both belong. Thank you."
Court is now a church pastor and says her stance against gay marriage - which was legalised in Australia in 2017 - derives from her religious beliefs.
In 2017 she wrote an open letter to Australian airline Qantas, saying she would be boycotting it because it had become an active promoter of same-sex marriage.
That same year she also said tennis was "full of lesbians", while she has spoken against transgender athletes and branded the teaching of LGBT rights as "of the devil".
McEnroe, who called Court a "crazy aunt", added: "Margaret Court is actually a ventriloquist, using the Bible as a dummy to say whatever she wants."
Tennis Australia said it would "recognise" the anniversary of Court's playing achievements rather than "celebrate" them.
The organisation distanced itself from her views, saying: "We cannot condone views that fracture our incredible tennis community, nor indeed the wider community."