It's alleged Mr Trump revealed highly-classified information about a plot, by self-proclaimed Islamic State, to top Russian officials during a meeting last week in the Oval Office.
The Washington Post newspaper cited what it said were current and former US officials as saying the disclosure potentially jeopardised a source of intelligence.
It's believed the information related to an IS terror threat linked to the use of laptop computers on aircraft.
It's also believed Mr Trump's alleged sharing of the information came before the US had shared it with its closest intelligence partners - the so-called Five Eyes alliance, which consists of the US, the UK, Canada, New Zealand, and Australia.
The group formed in the aftermath of the Second World War and acts as the intelligence eyes and ears of the western world, with a network of shared secretive, high tech surveillance stations and satellites that eavesdrop on telecommunications and internet traffic worldwide.
Associate Professor Patrick Walsh is with the Australian Graduate School of Policing and Security at Charles Sturt University.
He says the current geopolitical situation, together with Australia's involvement in the Five Eyes alliance, means it is of particular concern to Australia.
"It's obviously very concerning to the US intelligence community, and to the Five Eyes intelligence community, of which we are part. In general terms, yes, leaders talk about political events, and some of that draws from intelligence. But, if the allegation is true, it's terribly troubling at a time when the western relationship with Russia is at an all-time low, and there isn't anywhere near the level of trust that expect to allow that sort of thing to happen."
Mr Walsh claims this latest event will cause nervousness behind the scenes at high levels of Australia's intelligence community.
He says it won't ruin the intelligence relationship between Australia and its biggest ally - but it will raise alarm bells.
"Publically, political decision makers in Canberra wouldn't comment on this, but naturally, they'd be concerned, as would the Australian intelligence community. There's a long history of sharing intelligence with the US and other members of the Five Eyes, and that will survive this adminstration, because of the broader national interest for that to be the case. But it is deeply concerning, I would say, to people in Canberra, and there would be some reticience in terms of that sharing relationship, and some sort of risk management, risk assessment, going on, to the extent that that's possible in Canberra, about sharing intelligence. I wouldn't suggest for a minute that the tap is going to be turned off, because that's not in our interest. But there'll certainly be some reticence."
Mr Trump has previously clashed, very publicly, with his own country's intelligence community.
And Former Australian ambassador Kim Beazley told the ABC the intelligence or related communities in the U-S are not happy.
"Trump and his relationships are so comprehensively trashed, his standing with law enforcement and the intelligence community, that the normal level of quietness that emanates from them is no longer doing so."
The federal government has reacted cautiously.
Government minister Zed Seselja has told Sky News the US intelligence relationship is of great importance to Australia - and any concerns Australia has, won't be played out in public.
"The Five Eyes is very important for Australia. And we benefit greatly from those arrangements. And there is a significant degree of trust within that. And we've got no reason to doubt, or have concerns, about any of those issues. Of course, to the extent that there are issues in these relationships- and I'm not suggesting that there are- these would be expressed privately rather than publicly."
Russia's foreign ministry, meanwhile, says the reports are 'fake'.
