Education Secretary Alan Johnson has become the first cabinet minister to express interest in taking over from John Prescott as Labour deputy leader.
Mr Johnson stressed he was not launching a "campaign"
But he says until the job is vacant he is a "world away" from any "campaign".
And Mr Johnson tells ITV's GMTV Sunday Programme he "very much hopes" the under-fire Mr Prescott keeps the job.
Mr Prescott, meanwhile, is to undertake his only public role standing in for a holidaying Tony Blair when he chairs a meeting of environment ministers.
He is hosting a meeting of the British-Irish Council in east London before Mr Blair is expected to resume control of official duties later in the day.
Representatives from the British and Irish governments, the devolved administrations, Jersey, Guernsey and the Isle of Man will discuss the impact of extreme weather patterns and changing temperatures.
As environment secretary, Mr Prescott helped broker the Kyoto Protocol in 1997, committing countries to reductions in polluting carbon dioxide.
Mr Johnson's statement comes after Constitutional Affairs Minister Harriet Harman fuelled speculation about her own intentions when she said there should be two deputy leaders in future, one of whom should be a woman.
Mr Johnson said: "People have asked me if, when there is a vacancy, if I'd be interested in that vacancy and I've said quite honestly: yes, I would."
Mr Prescott continues to have use of the Admiralty House flat
However, he rejected speculation that he might one day become Labour leader.
Mr Prescott lost his department in a reshuffle after his affair with diary secretary Tracey Temple became public in April.
The prime minister has said Mr Prescott is to chair nine Cabinet committees and deputise for him on seven others but opposition parties say the row over him keeping his job is not at an end.
He initially kept his grace-and-favour homes - Dorneywood in Buckinghamshire and a London flat in Admiralty House - and his £133,000-a-year salary.
But on Wednesday he gave up Dorneywood in the wake of newspaper pictures showing Mr Prescott playing croquet.
The deputy prime minister later denied he had been playing while deputising for the prime minister saying the croquet game took place two days before Mr Blair went on holiday but accepted the scrutiny was "getting in the way" of his government job.
Aides said Mr Prescott had a "packed schedule" in Downing Street on Thursday.
And a number of Labour MPs hit the airwaves to welcome the Dorneywood concession and voice support for the deputy prime minister.
Mr Johnson, meanwhile, told GMTV the deputy prime minister "works harder than probably anybody I know".
"I don't want to get into the personal issues that happened around his family, that's a personal issue that he's already spoken of and dealt with a great deal of regret," he said.
"What I want to say is I think John Prescott is an excellent deputy leader of our party, he's been central to what our party has achieved since 1994, and I very much hope he stays as deputy leader."