Fairfax Media reported that the meeting would take place on board a battleship in New York Harbour and would underline the solidarity of the ANZUS treaty.
Federal government advisers, however, are reportedly split on the timing of the trip. The battle ran from May 4-8, and the federal budget is due to be handed down on Tuesday May 9.
An Australian official said: “The anniversary of the beginning of the battle falls on the Thursday before the budget, and there’s usually some major decisions left to the Thursday and Friday before the budget papers are printed on the weekend. It’s a moving feast.”
The news comes after Foreign Minister Julie Bishop met with US vice-president Mike Pence and US Secretary of State Rex Tillerson in Washington, DC.
Ms Bishop told News Corp Australia she invited Mr Pence to visit Australia “as soon as possible”.
Relationships between the two allies were rocked earlier this month when details of a heated call between Mr Trump and Mr Turnbull were made public.
Australian Minister for Foreign Affairs Julie Bishop met with US Vice President Mike Pence at the White House. Picture: Yuri Gripas Source:Supplied
However, Ms Bishop told Sky News that no-one has raised the call with her while she’s been in Washington.
“We are close friends, and that has been quite evident from my meetings with not only the administration officials but also the intelligence community and others with whom I’ve met during my time here in Washington,” she said.
On Thursday, Mr Turnbull and his British counterpart Theresa May compared notes on their contacts with Mr Trump since his inauguration last month.
The two prime ministers spoke by phone in a “substantial” conversation which also covered their hopes for a trade deal following Brexit, co-operation in the fight against Islamic State and relations with Iran, said the UK prime minister’s office, known as Downing Street.
Prime Minister Malcolm Turnbull and British counterpart Theresa May have spoken on the phone. Picture: Lyndon Mechielsen/News Corp
Reports earlier this month suggested that Mr Turnbull’s first phone call with the US president was a stormy affair, with Mr Trump supposedly criticising a deal to take migrants from Australia as “the worst ever” and ending the conversation abruptly.
But Downing Street said Mr Turnbull was “very positive” about his contact with Mr Trump in his conversation with May, while both agreed that her trip to Washington as the first foreign leader to visit the new president in January had been “positive”.
Ms May and Mr Turnbull, who were at Oxford University together, also discussed the campaign to defeat IS in Iraq and Syria and agreed on the importance of creating conditions to bring about long-term stability in Iraq.