The first Slam of 2020 will mark the 50th anniversary of Court winning all four majors in the same year - the holy grail of tennis.
Only two other women have achieved the feat - Maureen Connolly (1953) and Steffi Graf (1988). Don Budge was the first man in 1938, with the legendary Laver the only player to win it twice (1962 and 1969).
Court claimed a record 24 Grand Slam singles titles in total with only Serena Williams (23) and Graf (22) coming close, and one of the main courts at Melbourne Park is named after her.
Yet Court, now a church pastor, told the Sydney Morning Herald she had heard nothing from Australian tennis chiefs about honouring her at the tournament in January.
It follows controversy over her views on homosexuality and gay marriage, which has seen high-profile players like Billie Jean King and Martina Navratilova call for the arena to be stripped of her name.
"I think Tennis Australia should sit and talk with me," Court said. "They have never phoned me. Nobody has spoken to me directly about it. I think they would rather not confront it."
Court used to attend the Australian Open regularly but hasn't shown up since 2017, when the controversy first flared.
Fellow Australian Laver, who also has a stadium named after him at Melbourne Park, is routinely feted at the event and was honoured this year for his 1969 feat.
"They brought Rod in from America (where he lives). If they think I'm just going to turn up (in 2020), I don't think that is right," said Court
"I think I should be invited. I would hope they would pay my way to come like they paid for his (Laver), and honour me. If they are not going to do that, I don't really want to come."
Tennis Australia had no immediate comment to AFP, but told the Herald they were "in the process of working through" how Court's milestone would be recognised.
"As previously stated, Tennis Australia recognises the tennis achievements of Margaret Court, although her views do not align with our values of equality, diversity and inclusion," it added.
Court first drew fire in 2017 for saying she would avoid Qantas airline for its support of same-sex marriage, which is now law in her homeland following a referendum.
She later claimed tennis was "full of lesbians" and that transgender children were the result of a Nazi-style "plot" to brainwash the minds of young people.
"I don't feel any of that should be brought into my tennis career," Court told the newspaper.
"It was a different phase of my life from where I am now and if we are not big enough as a nation and a game to face those challenges there is something wrong."