Mr Trump signed an executive order on Tuesday morning Australian time, imposing a 25 per cent tariff on the products "without exceptions or exemptions".
It followed a phone call with Mr Albanese, the first between the two leaders since Mr Trump was sworn in, which the prime minister said was a "constructive and warm discussion".
Mr Albanese said he laid out the case for Australia to be exempted from the tariffs.
"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 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.
Speaking after signing an executive order enacting the tariffs, Mr Trump said the measure would bolster manufacturing in the US.
"It's going to bring our aluminium business back and make it go higher. It may go higher," he said.
However, Mr Trump said he would give Australia's case for an exemption "great consideration".
"We have a surplus with Australia. One of the few. And the reason is they buy a lot of airplanes. They're rather far away and they need lots of airplanes."
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."
