Similar to that call, the President's discussion with Morrison shows him using his position to advance his personal political interests.
READ MORE:
• Donald Trump goes on furious Twitter rant against Ukraine whistleblower and Democrats
• Donald Trump ordered hold on aid to Ukraine days before calling its leader, officials say
• World reacts as transcript of Donald Trump's call with Ukrainian leader is released
The FBI's counterintelligence investigation into Russian interference in the US election began after Australian officials tipped off the bureau about Mr Trump colluding with Russia to release damaging information on his opponent Hillary Clinton.
In late 2017, the Times reported that the FBI launched the investigation after Alexander Downer, Australia's former high commissioner to the United Kingdom, told US officials that Trump campaign foreign policy aide George Papadopoulos boasted to him that he had dirt on Hillary Clinton in the form of "thousands" of emails.
Papadopoulos told Downer he received the information from Joseph Mifsud, a Maltese academic who was last seen working as a professor in Rome before disappearing.
Papadopoulos has tweeted in response to today's bombshell report, saying he was "right about Downer from the beginning".
Addressing the Times report on ABC radio this morning, Downer said he has no knowledge of the latest revents about his role in the origins of the probe.
"I don't know anything at all about conversations Scott Morrison has had with Donald Trump," he said.
"I just have nothing more to say about it. I had a conversation with this guy (George Papadopoulos) and passed on one element about it," he added. "I can't offer you any more information.
"I know nothing of the conversations that Scott Morrison has had with the Americans, including President Trump about this, insofar as there have been any. I just don't have a clue."
Special counsel Robert Mueller's investigation confirmed Australia had played a central role in the origins of the FBI investigation, although his final report did not mention the country by name.
It said information from a "foreign government" prompted the FBI to "open an investigation into whether individuals associated with the Trump campaign were co-ordinating with the Russian government in its interference activities".
Morrison and Trump met in Washington last month for official meetings and a state dinner, which Barr attended.
In May, Trump told reporters he wanted his Attorney-General to examine all the countries he believed conspired to damage his chances at the 2016 election. He said he hopes Barr "looks at the UK, and I hope he looks at Australia, and I hope he looks at Ukraine. I hope he looks at everything, because there was a hoax that was perpetrated on our country".
According to Nine News, Australia's US ambassador Joe Hockey wrote to Barr in late May offering assistance in the Mueller inquiry review.