The BBC understands that if Andy Burnham becomes prime minister then he is expected to replace Rachel Reeves as chancellor and offer her a more junior cabinet position.
A spokesperson for Burnham said no decisions had been made.
It comes as the former Greater Manchester mayor begins to assemble a Downing Street team, assuming he wins the Labour leadership race in which, currently, he is the sole candidate.
Sir Keir Starmer announced he was standing down as prime minister days after Burnham won the Makerfield by-election, allowing him to return to Parliament.
The biggest decision Burnham will make as he begins to sketch out a possible cabinet is who will be his chancellor.
Most Labour MPs assume Reeves will not continue in that role but, as first reported by the Financial Times, external, she is expected to be offered a more junior cabinet position.
A close ally of Burnham told the BBC: “Andy really respects Rachel and I’m confident he’ll want her in his top team.”
James Purnell, who served as a minister in Gordon Brown’s government between 2007 and 2009, would be appointed Burnham’s Downing Street chief of staff.
But if the new MP for Makerfield becomes prime minister, how much to spend on defence will be an immediate challenge.
Burnham and his team have been discussing that with John Healey, the former defence secretary, who resigned earlier this month, warning the current planned increase in military funding fell “well short of what is required”.
