Wes Streeting "won't fight" Andy Burnham if he wins the Makerfield by-election as "no one can beat" him if he makes it back to Parliament.
Insiders who have worked with Mr Streeting have indicated there is a growing feeling of the Greater Manchester mayor being unbeatable in a leadership challenge for the top job.
However, a different source dismissed the rumours as "rubbish", arguing the former Health Secretary is focused on the challenge at hand, come what may.
Yesterday, Mr Streeting said he had "no regrets" after stepping down from the frontbench and put his support behind Mr Burnham, also a former Health Secretary, but under Gordon Brown, in the Makerfield by-election.
Reading out his resignation statement to the House of Commons, Mr Streeting painted a bleak picture for Labour unless it changed its direction as it was losing the fight against "nationalism".
He said: "We risk handing the keys of No10 to Reform.
"This is our fight. It's Andy Burnham's fight in Makerfield and it is Labour's fight for the soul of our country."
Wigan Council confirmed yesterday the Makerfield by-election will take place on Thursday, June 18.
Great British Summer Savings scheme is 'absurd', says Shadow Chancellor
Shadow Chancellor Mel Stride called the Government's package to ease the cost of living is "absurd", having little impact and accused the increasing cost of living being down to some of the Government's own policies.
Speaking to GB News, he said: "If the price of anything comes down through lower tariffs or taxes, then that will ease things very, very, very slightly, but to the extent that people are going to be benefiting from slightly cheaper chocolate bars, dried fruit, or peanuts, I think is a fairly debatable point.
"The fundamentals here are that we've got our economy in a position where we've had low growth, very high taxes, which is causing people to have to tighten their belts from high and rising unemployment and high inflation across the period that this Government's been in office and their policies have fed into all those problems.
"That's why we're in a weaker position now to lean into the challenges of higher oil and gas prices due to the Middle East conflict than we would otherwise have been."
Green Party announces Makerfield candidate
The Green Party have announced their Makerfield by-election candidate as Chris Kennedy, a children's safeguarding specialist, who said he was "proud" to have been selected to stand.
He said: "We want to defend our area against the politics of hate and division and bring people together around a positive vision for the future.
"At the same time, we can’t let this election be dominated by a Westminster psychodrama. It must be about protecting what makes Makerfield special. People here are feeling the pressure of the cost-of-living crisis, and they deserve real support.
"Greens will fight for warmer homes, lower bills, and a fairer economy. And we will always stand up for our NHS, properly funded, publicly owned, and there for everyone when they need it."
Labour has 'world-leading sanctions regime' despite lifting Russian oil restrictions, says Lucy Rigby
Chief Secretary to the Treasury Lucy Rigby pushed back firmly against suggestions the Government is softening its stance on Russia after some sanctions on Russian oil were lifted, insisting the broader package announced this week makes life significantly harder for Vladimir Putin than it did last week.
Speaking to GB News, she said: "The sanctions that we've got in place today as a result of the package that's been announced are much tougher than they were last week.
"We have a world-leading sanctions regime. We've already sanctioned 3,300 Russian individuals, entities and businesses, and our support for Ukraine is absolutely steadfast."
Lucy Rigby: Labour 'understands family budgets are stretched'
The Treasury is due to set out a package of measures today which are designed to ease pressure on family budgets, including free unlimited bus travel for children in England throughout August, the removal of tariffs on around 125 agri-food products to help reduce the cost of the weekly shop and a continued freeze on fuel duty following the Prime Minister's announcement yesterday.
Lucy Rigby, Chief Secretary to the Treasury told GB News: "This package altogether is all about trying to help families right across this country with the cost of living, because we understand that family budgets are stretched at the moment.
"This comes on the back of a whole host of things we've been doing as a government - raising the minimum wage and the national living wage, freezing rail fares, freezing prescription charges."
What is happening in Westminster today?
Good morning, happy Thursday from the Politics Team at GB News.
Today, we are expecting to hear from the Chancellor Rachel Reeves on her Great British Summer Savings Scheme - which we expect to see tariffs cut on some food imports and free bus travel for children in August.
What we are not going to see if food price caps enforced on the supermarkets, after Ms Reeves backed down from the idea when retailers and the Bank of England pushed back on the idea.
We have already heard from Lucy Rigby MP, Chief Secretary to the Treasury (update to come) and we'll be hearing from Shadow Chancellor Mel Stride in just under an hour.
Stay tuned for more politics updates throughout the day.