Trump asked Morrison to help find evidence to discredit the inquiry, the BBC quoted US and Australian media reports as saying on Tuesday.
Australia confirmed the call had taken place and that Morrison agreed to help.
The transcript of the call between Morrison and Trump was restricted within the White House to a small number of the President's aides, the reports said - contrary to normal protocol.
In a statement on Tuesday, the Australian government said it had "always been ready to assist and co-operate with efforts that help shed further light on the matters under investigation".
"The Prime Minister confirmed this readiness again," the statement said.
Australia's conservative leader is among Trump's closest international allies and received the rare honour of a state dinner at the White House last week.
The revelation comes as Trump faces impeachment proceedings over a call with Ukrainian President Volodymyr Zelensky, the BBC reported.
Trump is accused of repeatedly pressuring Zelensky to investigate former Vice President and 2020 Democrat candidate Joe Biden, in a phone call which was exposed by a whistleblower last week.
The call spurred House Democrats to launch impeachment proceedings, and on Monday the President's lawyer Rudy Giuliani was served with a subpoena.
The Mueller inquiry investigated whether Trump colluded with Russia in the 2016 presidential election. Its findings, released in April, did not establish that the Trump campaign criminally conspired with Russia to influence the election.
But the findings did not exonerate the president of collusion, and the Mueller report outlined an extensive obstruction-of-justice case against the President.
( With inputs from IANS )