The two leaders could meet on the sidelines of the G7 summit in Canada next week, with the economic measures imposed by Mr Trump around the world set to dominate discussions.
As Australia looks to negotiate for an exemption on tariffs, Trade Minister Don Farrrell was optimistic a deal could be reached.
"I certainly haven't given up on the prospect of getting these tariffs removed, and every opportunity I get, I'll continue to pursue that argument with the United States," he told Sky News on Sunday.
"There is no justification for the United States to impose tariffs on Australia ... we want all of the tariffs removed, not just some of them."
Mr Trump recently signed off on doubling tariffs on exports on steel and aluminium from 25 to 50 per cent.
All other Australian exports to the US have been slapped with a 10 per cent tariff.
But opposition finance spokesman James Paterson said any meeting between the prime minister and US president should have happened sooner.
He said an exemption on steel and aluminium secured by the UK showed it was possible Australia could receive a similar outcome.
"Australia is at least as good an ally of the United States as the United Kingdom is and so there's no reason why the prime minister shouldn't at least be able to secure that exemption," Senator Paterson told ABC's Insiders program.
Senator Farrell met with US trade representative Jamieson Greer last week and said he pushed the case for all of the economic measures to be removed.
The minister was hopeful a similar approach that removed $20 billion worth of tariffs on Australian goods entering China could be used with America.
"We didn't retaliate on that occasion, and bit by bit, we managed to get all of those tariffs that had been applied on Australia by China removed. I'd like to do the  same with the United States," he said.
"It's only by open discussion, honest discussion with out allies in the United States that I think we can do that."
Senator Paterson said the coalition would be open to the idea of a critical minerals stockpile that could be used as a bargaining chip in any tariff negotiations.
"It is something that Australia could do which would represent an economic opportunity and a strategic contribution," he said.
As the US Defence Secretary Pete Hegseth urged Australia to increase its defence spending by billions of dollars to 3.5 per cent of GDP, Senator Farrell said the federal government had already proved its commitment through the AUKUS submarine deal.
Australia is looking to up its total spent on defence to 2.3 per cent.
"We are committed to the defence of this country, we are committed to a significant uplift in the amount of spending," Senator Farrell said.
"(AUKUS) is going to be a project that's worth more than $360 billion, so I think we've talked the talk."
Senator Paterson said the opposition was still committed to its election platform of increasing defence spending to three per cent.
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