David Miliband has fuelled rumours of a shock comeback as Andy Burnham prepares to take power within weeks.

The former Foreign Secretary pointedly refused to rule out a Cabinet return when he was asked directly at an event last night, merely saying Mr Burnham would 'make his own choices'.

Mr Miliband - currently head of New York-based aid agency the International Rescue Committee - also said he believed the incoming PM would go further on unwinding Brexit. 

Despite taking home a salary of around £1m himself, Mr Miliband complained that European countries had a problem with wealth being 'very unequally distributed'.

Speculation has been swirling about Mr Miliband, who quit UK politics after losing the 2010 Labour leadership election to his younger brother Ed.

There are questions within the party over whether the pair could work together. Ed Miliband has been lobbying to be made Chancellor in a Burnham administration, raising the possibility of siblings holding two of the great offices of state for the first time in modern politics. 

Mr Burnham and the Milibands were all advisers in Tony Blair's New Labour project, before becoming MPs. 

Pressed at an Institute for Government event last night whether he would accept a job from Mr Burnham, Mr Miliband laughed and said: 'Let him make his choices. Give him the space to form his Government.' 

On a separate podcast with Politico, Mr Miliband said he wanted to see a more determined effort to get closer ties with the EU.

'I certainly think the deficiencies of Brexit are still being played out. Brexit has been bad for Britain but I would also argue it has been bad for the rest of Europe, it has been bad for the EU,' he said.

'I think that the ambition of a reset that was set by the Starmer administration was right, but the dosage was too low. It didn't have the momentum or the heft, or the coherence, or the ambition sufficiently behind it.

'I am very hopeful that Andy Burnham recognises that. I think he will be very very clear that British prosperity and security depends on engagement with Europe rather than separation from the rest of Europe.

Mr Miliband was also asked about international aid contributions being cut. While acknowledging that ordinary people were feeling the pinch across Europe, he suggested that was partly because wealth was 'very unequally distributed'.

Mr Miliband would require a peerage in order to take a Cabinet job, assuming he did not attempt to become an MP again. Foreign Secretary is regarded as most likely, with echoes of David Cameron's comeback to the role under Rishi Sunak.

Mr Burnham could be confirmed as PM by 6pm on July 15, under a timetable announced by Labour yesterday.

MPs' nominations for the party leadership are due to close at that time, meaning the former Greater Manchester Mayor should know whether anyone else is challenging.

Former defence minister Al Carns is the only senior figure still openly considering standing, although he seems to be focused on gaining leverage for more military funding. 

The schedule laid out by Labour's ruling NEC would see Mr Burnham formally take over from Keir Starmer in No10 two days later.

The plans have been finalised as Sir Keir insisted he wants to 'minimise disruption' and behave with 'good grace' following his resignation on Monday.

The outgoing premier also pointedly claimed he was 'leaving the country in a better position than when I found it', after being effectively forced out by pressure from MPs. 

Labour figures have been frantically jockeying for position in the new team, with Rachel Reeves seemingly doomed to losing her spot in No11.

Unions, businesses and some Labour moderates have been fighting a rearguard action to stop Ed Miliband entering the Treasury. 

Other candidates for the job include Home Secretary Shabana and Yvette Cooper - currently Foreign Secretary. 

Longstanding allies of Mr Burnham including Louise Haigh are in line for big promotions.