The United Nations security council has approved a plan that opens a pathway for an international force to enter the strip, in addition to a governance board to provide oversight of the war-torn territory during reconstruction efforts.
The prime minister said he had received correspondence from the White House overnight and would consider the request.
"We'll consider all of these approaches respectfully and through our proper processes," Mr Albanese told ABC radio on Monday.
But the Labor leader added he was yet to look into the details of the request as he had been focused on parliament returning to debate hate speech laws following December's massacre at Bondi.
Mr Trump has invited other world leaders to join the board including Canadian Prime Minister Mark Carney, Turkish President Recep Tayyip Erdogan and Egyptian President Abdel Fatah al-Sisi.
Other names put forward for the board, which the US president will chair, include US Secretary of State Marco Rubio, former British prime minister Tony Blair and Mr Trump's son-in-law, Jared Kushner.
Defence Minister Richard Marles said the government would be discussing the proposal with the US.
"We certainly welcome the invitation, as we do welcome terms of the specific request, we'll continue to talk that through with America to properly understand what this means and what's involved," he told ABC TV.
Israel has said it is opposed to some of the world leaders joining the board, although it did not specify which inclusions it rejected.
Its government said several of the proposed appointments were "not coordinated with Israel and were contrary to its policy".
The Trump administration has reportedly asked countries to contribute at least US$1 billion to become permanent board members.
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