Andy Burnham will attempt to return to the Commons as an MP, after Wes Streeting resigned as health secretary, saying he had lost confidence in Prime Minister Sir Keir Starmer's leadership.
Burnham, the Greater Manchester mayor, said he would ask to run for Labour in Makerfield after Labour MP Josh Simons said he would resign to make way for him.
Any candidate in a Labour leadership contest to replace Sir Keir must be an MP.
Streeting called for a broad debate about what comes next but did not say he would run for leader.
Speculation has been rife over Sir Keir's future as leader following a disastrous set of election results for Labour last week. No leadership challenge has been triggered.
Earlier on Thursday, former Deputy Prime Minister Angela Rayner, also seen as a potential challenger to Sir Keir, said she had resolved her tax affairs with HMRC.
Announcing he would stand down, Simons said he believed Burnham could "drive the change our country is crying out for".
Burnham said he would seek people's support to return to Parliament in order to "bring the change we have brought to Greater Manchester to the whole of the UK and make politics work properly for people".
He would, he added, "not take a single vote for granted" and would "work hard to regain the trust of people" in the north-west constituency, which Labour held in 2024 with a majority of 5,399 votes over Reform UK.
Reform leader Nigel Farage said the party looked forward to the contest and would "throw absolutely everything at it" after giving Labour a drubbing at the recent council elections in the area.
Burnham was blocked by Labour's ruling National Executive Committee from contesting the Gorton and Denton by-election in February, which Labour lost to the Green Party.
The BBC understands Sir Keir will not seek to block Burnham from becoming the Labour candidate in Makerfield.
An ally of Sir Keir said he was "focused on bringing the party together so it can tackle the issues facing working families".
The by-election date is yet to be announced and depends on when the government triggers the formal process.
Streeting became the first cabinet minister to resign, blaming the "unpopularity of this government" for Labour's poor results in last week's elections.
He said: "Leaders take responsibility, but too often that has meant other people falling on their swords."
Streeting said the country faced big challenges "that require a bold vision and bigger solutions than we are offering".
Education Secretary Bridget Phillipson said Streeting had done "a fantastic job" as health secretary but that she disagreed with position he had taken.
There was no mention of a possible leadership challenge from Streeting, although his camp insisted he had enough support from MPs to trigger one - a claim disputed by an ally of Sir Keir.
Labour MP Alan Gemmell, who supports Streeting, told BBC Radio 4's World at One programme Streeting had "taken a principled decision today not to trigger a contest".
The MP added: "It's clear in conversations with MPs and with the unions that the party wants a discussion, a battle of ideas, an open contest, a broad contest for the direction that we should take and how we fix the problems that we're in."
Downing Street announced on Thursday evening James Murray would be Streeting's successor as health secretary, moving from his role as chief secretary to the Treasury.
Rayner announced she had resolved her tax affairs with HMRC following an investigation, settling £40,000 in unpaid stamp duty.
Rayner said she had been "exonerated" of the accusation she had "deliberately sought to avoid tax".
She had stood down from her cabinet roles last September after admitting she underpaid stamp duty on her £800,000 flat in Hove.
On Thursday morning Rayner told the Guardian newspaper she did not rule out running in any Labour leadership race but that she would not "trigger" a contest.
She said: "I'll play my part in doing everything we possibly can to deliver the change, because it's not a personal ambition, I know the difference it makes."
An MP wanting to force a leadership election in a bid to remove Sir Keir would require 20% of the party's MPs to back a replacement candidate.
There are 403 Labour MPs, so the support of 81 would be needed.
Sir Keir would not be required to gather support as he would be automatically on the ballot paper if he chose to contest the leadership election.
On Friday, Labour's deputy leader Lucy Powell is expected to say Burnham, Streeting and Rayner should all be "key players" in Labour's team when she speaks at the Fire Brigades' Union conference.
