Almost a year into Mr Trump's second term in office, Mr Albanese has struggled to organise face-to-face talks with the Republican leader, after a planned meeting in Canada in June was cancelled at the last minute because of escalating Middle East tensions.
However United States Studies Centre director of research Jared Mondschein says it appears the two will sit down on the sidelines of the United Nations "leaders' week," which starts on September 22.
"Especially with this administration, the personal really goes a long way ... so I think it is something that the prime minister does want to focus on," he told AAP.
A readout of the call released by Mr Albanese's office said the two leaders discussed trade and critical minerals - a conversation Mr Mondschein said was "timely" as China restricts exports of metals such as lithium and cobalt.
China dominates global production of critical minerals, which are used in products such as electric cars, solar panels and some defence technologies.
Australia, which has massive underground reserves, hopes to break China's stranglehold.
While critical minerals were previously offered as part of a deal with the US to try to get a lower import tariff, Resources Minister Madeleine King told the ABC "critical minerals sits on its own".
"We are in the best place in the world to be able to mine and refine those commodities - there's no swap on these things," she said.
Australia needed to think about its relationship with the US in developing these rare earth supply chains "because it's a really tall order to establish this industry".
"We saw a really very significant moment a few weeks ago when the US Department of Defence invested a significant amount of money in introducing a floor price into a light rare earths mine," Ms King said.
"We want to work with them on how we might have a similar system, or they might invest in US strategic reserve to make sure we lift all boats on that tide so we can create that rare earth industry that the world needs to have a diversified supply chain."
Australia was "looking at a range of things" through critical mineral strategic reserve offtake agreements, Ms King said.
"A floor price may be part of that, a stockpile of sorts. And all of these things can work together to introduce stability into a market that is subject to intensive manipulation."
Asked if a face-to-face meeting with Mr Trump was closer, Ms King said she had "no doubt that meeting will happen but it will be off the back of a number of close phone calls and other interactions with the US Administration".
There was no mention of the AUKUS nuclear submarine deal in the Australian readout of the call with Mr Trump but the government insists the military agreement with the US and UK will go ahead, despite the White House's decision to review it.
"It is on schedule and we are really confident about its progress," Defence Minister Richard Marles told reporters in Tokyo after meetings with Japanese officials.
The opposition has long criticised Mr Albanese's failure to secure a meeting with Mr Trump.
"It's been more than 300 days since the US election, yet the prime minister has not secured a face-to-face meeting with the president, who has already met with over 30 other world leaders," opposition trade spokesman Kevin Hogan said.
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