According to a New York Times report, Trump in a recent phone call asked Morrison to gather information for the US Justice Department probe into the origins of the counterintelligence investigation of the Trump campaign in 2016.
"The Australian government has always been ready to assist and cooperate with efforts that help shed further light on the matters under investigation," the government said in a statement on Tuesday morning, as quoted by The Guardian, adding that Morrison "confirmed this readiness once again in conversation with the [US] president."
On Monday, US Justice Department Spokeswoman Kerri Kupec said in a statement that US Attorney General William Barr had asked Trump to contact foreign states to introduce the department’s team investigating the origins of the Mueller probe.
According to Kupec, US Attorney John Durham was gathering information from numerous sources, including a number of foreign countries.
US Special Counsel Robert Mueller issued a final report on his inquiry in April, saying the probe had found no evidence of collusion between Trump and Russia during the 2016 presidential campaign.
Trump has become embroiled in a political scandal after a US government whistleblower claimed the president had pressured Ukrainian President Volodymyr Zelenskyy during a July phone call to look into a corruption case involving 2020 Democratic presidential candidate Joe Biden and his son Hunter.
The US Democrats have launched impeachment proceedings against Trump, saying he sought to pressure a foreign government into assisting his re-election campaign. Trump denies any wrongdoing and has accused Democrats of launching another "witch hunt" against him.