At least two senior Labour MPs are considering launching leadership bids to prevent Andy Burnham becoming prime minister without a formal contest.
Former defence minister Al Carns has said he is weighing up whether to run, while Sir Keir Starmer's Chief Secretary, Darren Jones, has also not ruled out a challenge, BBC News understands.
Labour MPs increasingly believe Burnham could become prime minister as early as 17 July - the day after nominations for the new leader close - after Sir Keir announced his resignation on Monday.
However, a large contingent are uncomfortable with the idea of a leader whose policy ideas have not been tested in a leadership race.
Some MPs are urging Jones - a close ally of Sir Keir - to stand. It is considered unlikely but Jones is understood not to have ruled it out.
Carns - who was the armed forces minister until he resigned earlier this month over defence spending - also indicated he was interested in a tilt at the top job.
"I'm not ready to make a decision on this in any way shape or form," he told ITV's Peston on Monday night.
"What I would say is we need to move from the politics which talk through the tactics and think about the strategy and what I'm really looking for are big objective outcomes that we want to get to in 2029 and 2034/35".
Sir Keir said he had asked Labour's governing body to set out a timetable to replace him, with nominations opening on 9 July and ending by the summer recess on 16 July.
Potential candidates have until then to amass the support of at least 81 Labour MPs.
Burnham is seen by many as the frontrunner to replace Sir Keir after an emphatic victory over his Reform UK rival in last week's Makerfield by-election.
The former Greater Manchester mayor, who was formally sworn in as an MP in the House of Commons on Monday, said he would put himself forward as a candidate in the leadership contest.
Wes Streeting had been viewed as his main rival but the former health secretary was quick to offer his support to Burnham, increasing the likelihood of a "coronation".
John Slinger, the Labour MP for Rugby, voiced the feelings of many within the party who believe it is "necessary" to have a full leadership contest.
"I think the public out there would think we'd slightly lost our minds if we didn't go through a process where we subject people who aspire to the highest office in the land to completely normal scrutiny," he told the BBC's The World Tonight on Monday.
Describing Sir Keir as a "terrible prime minister", Conservative Party leader Kemi Badenoch attacked the Labour Party's policies, saying: "Labour MPs only want higher taxes to hand out more benefits... These are Labour's choices and their values, regardless of who is running the party."
Liberal Democrat leader Sir Ed Davey said the British people were "sick of being let down by an endless merry-go-round of prime ministers while nothing really changes".
Reform leader Nigel Farage demanded a general election, saying: "If Labour thinks it can shove another professional politician into No 10, it has another thing coming."
Zack Polanski, leader of the Green Party of England and Wales, said people would hope that Burnham could bring about "meaningful change" but the "jury is out".
Hoping to fill in some of the blanks currently in his policy agenda, Burnham is expected to give a speech next week promising to grow the economy if he becomes PM, while also sticking to the government's fiscal rules.
Those rules aim to restrict borrowing and pay for day-to-day spending out of tax revenues by the end of the decade.
Burnham's allies say he is yet to decide who would be his chancellor, with one source saying: "No jobs have been given and no deals made."
Sir Keir was elected leader of the Labour Party in April 2020 and became prime minister on 5 July 2024 following Labour's landslide general election victory.
His decision to step down means the UK will soon have its seventh prime minister since 2016.
On Monday evening, Sir Keir and his wife Victoria hosted No 10 staff for drinks in the No 10 garden, where they thanked those present for the support they had given.
