The prime minister will be in New York for the UN General Assembly, with bilateral meetings on the cards throughout the week.
While a formal one-on-one has not been confirmed, Mr Albanese will have the chance to come face-to-face with Mr Trump at a gala reception hosted by the US president during the high-level week.
As the prime minister makes the case to world leaders for further measures to rein in AI as part of digital reforms, Mr Trump has said concerns of the rising technology have been a "hoax".
The US president has said a slowdown in the AI race by the United States could involve the country losing ground to China.
Mr Albanese said he would put concerns about AI to Mr Trump.
"We have a view about artificial intelligence that there needs to be appropriate safeguards put in place, and I will advocate that privately, the same as I will publicly," he told reporters in New York on Monday, Australian time.
"I have a very positive and constructive relationship with the president, and I will engage respectfully and constructively with him."
The prime minister has been hopeful other countries could be able to work together at the UN to put in place regulations on the AI sector.
He raised those concerns with former Apple chief executive Tim Cook during a closed-door discussion at the tech company's headquarters in California on Sunday, Australian time.
The federal government is set to introduce legislation later in the year for national AI standards.
Mr Albanese has left the door open for a model that would allow creators to opt out of their work being used to train or otherwise inform AI.
Copyright laws have been flagged as a potential hurdle for AI companies with plans to invest in operations in Australia.
The push at the UN coincides with OpenAI head Sam Altman and Anthropic chief executive Dario Amodei calling for a slowdown in the technology's development.
Mr Albanese said he would also advocate with Mr Trump for a de-escalation of the war with Iran, which has caused global oil prices to surge.
"We need to see (a de-escalation) because this is having a massive impact on the global economy, which effects Australians," he said.
"This is having an impact on global inflation and the global economy."
Mr Albanese and Mr Trump held a phone call in August, where the war in Iran and tariffs imposed by the US on Australia were discussed.
