Turnbull wrote in a 1994 book "The Reluctant Republic" that it was "difficult to believe that Prince Charles could ever be accepted as king".
'Thank goodness the gardens are still here and it hasn't been built on, ' the prince said.
Prince Charles and Camilla will touch down in Brisbane on Wednesday, with Boeing 737-BBJ airliners in the RAAF's VIP fleet to transport the pair for their tour of the country.
Charles has declined a cheeky invitation to explain why he, and not an Australian, should become the nation's next head of state in a speech during his Australian visit.
Her 69-year-old eldest child arrived in Australia while the country's relationships with Britain and its monarchy are under renewed scrutiny. "As far as the republic is concerned, or Australia's constitutional arrangements, as the prince has always said and indeed the queen has always said, it's a matter for Australians", Turnbull told Australian Broadcasting Corp. on Tuesday.
The former PM, who discussed Australia's status with Prince Charles in Scotland in 1993, believes it can not claim to be a "great" nation while "borrowing" Britain's monarch.
Mr Keating, who was prime minister of Australia from 1991-1996, has long supported a republic.
"Prince Charles would just want to do his duty and he shouldn't be verballed by an ex-PM", the former Liberal prime minister and now right-wing backbencher posted on Twitter.
Prince Charles' bill for his 2012 trip Down Under was a tidy $437,057.
"It'd be wonderful if he'd come out and say that outright, not that we have an actual expectation of that".
The heir to the British throne inspected the royal guard of honour and God Save the Queen and the Australian anthem were performed.
Prince Charles and his wife Camilla have touched down in Brisbane for the start of their official visit, which will include opening the Gold Coast Commonwealth Games tonight.
"People are entitled to protest and we have no issue with that", Mr Beattie said.
On Friday the Prince of Wales will travel to Bundaberg to attend The Big Bundy BBQ, a community celebration at the Bundaberg Rum Distillery hosted by Premier Annastacia Palaszczuk.
"I'll be asking him how much he's looking forward to the Commonwealth Games", she told reporters on Monday.