The BBC understands that if Andy Burnham becomes prime minister he is expected to replace Rachel Reeves as chancellor and offer her a more junior cabinet post.
A spokesman for Burnham said no decision had been made.
It comes as the former mayor of Greater Manchester has begun to assemble his Downing Street team, believing he has won the Labor leadership race in which, at present, he is the only candidate.
Days after Burnham won the Makerfield by-election, Sir Keir Starmer announced he was stepping down as Prime Minister, allowing him to return to Parliament.
As Burnham begins to outline a potential cabinet, the biggest decision will be who will be her Chancellor.
Most Labor MPs believe Reeves will not remain in the role, the Financial Times first reported, externalHe is expected to be offered a more junior cabinet post.
A close associate of Burnham told the BBC: “Andy really respects Rachel and I’m sure he would want her in his top team.”
James Purnell, who served as a minister in Gordon Brown’s government between 2007 and 2009, is to be appointed Burnham’s Downing Street chief of staff.
But if Makerfield’s new MP becomes prime minister, how much will be spent on defense will be an immediate challenge.
Burnham and her team are discussing why former Defense Secretary John Healey, who resigned earlier this month, warned that the current planned increase in military funding “falls well short of what is needed”.
