Mr Trump enacted an executive order on Tuesday morning Australian time imposing a 25 per cent tariff on the products.
The signing came after a phone call between the US president and Prime Minister Anthony Albanese, the first between the two leaders since Mr Trump was sworn in in January.
Mr Albanese said he laid out the case for Australia to be exempted from the tariffs, describing the call as a "constructive and warm discussion".
"We agreed on wording to say publicly, which is that the US president agreed that an exemption was under consideration in the interests of both of our countries," Mr Albanese told reporters in Canberra.
"We'll continue to engage quite clearly, constructively."
Mr Trump imposed similar tariffs on steel and aluminium during his first term in 2018, but Australia was able to secure an exemption from the measure shortly after it was enacted.
The US president said Mr Albanese was a "very fine man" and that he would examine an exemption, despite the order applying to all countries.
"We have a surplus with Australia, one of the few, and the reason is they buy a lot of airplanes," he told reporters at the White House.
"I told (Albanese) that that's something that we'll give great consideration to."
The prime minister said he reminded Mr Trump that the US had a trade surplus with Australia going back decades.
"What I envisage is continuing to act to respond diplomatically. That's how you get things done.
"My government's got a record of getting things done in Australia's national interest, I'll continue to do so," he said.
Opposition Leader Peter Dutton stressed bipartisanship from Australia on the need for an exemption to any looming tariff.
"I want there to be a very clear message to the Trump administration that we believe this tariff should not be put in place and if it remains in place I believe it would damage the relationship between the United States and Australia," he told reporters in Canberra.
"I don't think (the tariffs are) warranted, and I strongly support so the prime minister in his call for the tariff to be reduced."
Despite previous criticism of Australia's ambassador to the US Kevin Rudd over his previous comments about Mr Trump, the opposition leader said he backed the job he was doing in Washington.
"I assume that he's getting access to the White House and to key administration figures, and I presume that that he has a functioning relationship with the chief of staff," Mr Dutton said.
Mr Albanese said he was confident about a deal being struck.
"If you have a look at what we've achieved already, it's been a tremendous start to the relationship," he said.
"The relationship is in good shape."
The pair also discussed critical minerals and Australian Jordan Mailata being part of the Philadelphia Eagles, who won the NFL Super Bowl on Monday.
Treasurer Jim Chalmers said the tariffs on steel and aluminium were significant, but not surprising.
"We expect changes in policy from a new administration. We're confident that we can navigate them," he told reporters in Canberra.
"We all are well placed and well prepared to deal with announcements coming out of DC, and part of that effort is engaging directly, as the prime minister has this morning, with President Trump."
