Mr Albanese locked in an in-person meeting with Mr Trump for October 20 at the White House while he was in the US for the United Nations General Assembly.
The confirmation of the October bilateral followed Mr Albanese meeting with Mr Trump for the first time at a gala dinner hosted by the US president for world leaders at the UN summit.
Mr Albanese said he did not feel the need to present Mr Trump with an offering at their meeting, as other world leaders have during White House talks, but said the relationship between the two countries was strong.
"I feel like I need to treat (Trump) with the respect that the president of the United States deserves, and I expect that to be returned," he told ABC's Insiders program on Sunday.
"We've had five either phone conversations or greetings in person now, and they've all been warm, constructive, positive and optimistic.
"It is in both Australia's interests and the interests of the United States that we continue to have a good relationship."
A potential deal on tariffs is expected to be on the agenda for the meeting, as well as the future of the AUKUS deal, with the US undertaking a review of the trilateral security pact that would give Australia nuclear submarines.
Mr Albanese signalled supplies of critical minerals from Australia to countries such as the US could also factor in negotiations.
"Critical minerals could become certainly (part of AUKUS), because a range of the equipment, what's required for defence of all of our three nations, will be critical," Mr Albanese said.
"Minerals will play a role in that. What we are talking about is making sure that we maximise the return to Australia."
Australian officials are still trying to determine the full impact of the latest round of tariffs imposed by Mr Trump on pharmaceuticals imported to the US.
The president said a 100 per cent tariff would be placed on branded or patented pharmaceutical product imports from October 1, unless a pharmaceutical company was building a manufacturing plant in the US.
Pharmaceuticals are one of Australia's biggest exports to the US, worth $2.2 billion, and there are fears the Australian biotech company CSL could be affected.
Health Minister Mark Butler said work was under way to determine how the tariffs would impact Australian goods.
"The vast bulk of our exports to the US are actually blood and plasma products, so it's not entirely clear whether they are captured by the scope of the announcement the president made," he told Sky News.
"There's a very high likelihood the major exporter that accounts for the vast bulk of our exports to the US will not be captured by this new announcement."
Opposition foreign spokeswoman Michaelia Cash said tangible results needed to come from the talks between Mr Albanese and President Trump.
"Australians don't expect their prime minister to be scared. They expect their prime minister to deliver outcomes," she told Sky News.
"The relationship in Washington is not strong, and because it's not strong, Mr Albanese is not able to pick up the phone, like other world leaders are able to do, and speak directly to the US president about the impact of (the tariff) announcement on Australia."
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