Keir Starmer has been offered a place on the Gaza “peace board” set up by Donald Trump as part of the ceasefire agreement between Israel and Hamas.

The prime minister was asked to sit on the board by a senior member of the Trump administration. The Guardian has been told that Starmer is expected to accept but has not yet received a formal invitation, while conversations about the exact makeup of the board are continuing.

Starmer has cultivated a good relationship with the US president, despite their differences of opinion on the UK’s decision to recognise the state of Palestine last year.

The board is expected to temporarily oversee the running of Gaza and manage its reconstruction. It will be made up of world leaders, with US media reports suggesting Trump could announce its membership as early as this week.

Tony Blair was initially expected to be on the board, which will be chaired by Trump himself, with the former Labour prime minister saying the US plans were “the best chance of ending two years of war, misery and suffering”.

But Blair, who is viewed with scepticism and hostility over his role in the disastrous US-led invasion of Iraq in 2003, was quietly dropped from consideration after some Middle Eastern nations objected to his involvement.

Speaking to reporters onboard Air Force One on Sunday, Trump said the peace board was in the process of being formed, and there was strong international interest in being involved.

“Essentially, it’s the most important leaders of the most important nations. You take the most important leaders and nations, that’s who the board of peace is going to be,” he said.

In the Commons on Tuesday, the foreign secretary, Yvette Cooper, was asked if Starmer had joined Trump’s peace board. “We supported the 20-point plan to achieve a ceasefire in Gaza,” she said.

“That is still fragile and there’s still a huge amount of work to do, including humanitarian surge and support, and including the decommissioning of weapons from Hamas.

“There’s a huge amount of work still to do but it’s really important that the whole international community comes together in order to support that.”

Starmer has defended his frequent trips out of the country, and on Monday night attempted to draw a direct link with the cost of living at home, which he told Labour MPs would not be solved by isolationism.

The prime minister told them that it was essential for him to be “in the room” for international negotiations on trade and defence, which would then have an impact on the domestic economy.