John Prescott has suggested Tony Blair could "follow the example of Harold Wilson" who stood down mid-term, reports the Evening Standard.
Tony Blair has refused to comment on speculation over his future
Mr Prescott said Mr Blair would have Labour's full support if he led the party into the next general election.
But he hinted that the prime minister could be derailed by "events".
His remark follows earlier comments by the deputy prime minister suggesting cabinet ministers were jockeying for position in case Mr Blair stood down.
Asked to explain his latest remarks, Mr Prescott said: "I am convinced, though, from my talks with Tony, of course, that he would like to lead us into that election.
"But he always considers events, events, events."
That was taken to be a reference to Tory premier Harold Macmillan, who when asked what would most easily steer a government of course, famously said: "Events, dear boy, events."
Mr Blair refused on Tuesday to say whether he intends to serve a full third term if he wins the next election, dismissing speculation as a Parliamentary "parlour game".
Senior ministers have repeatedly insisted the prime minister has no plans to step down.
Mr Prescott was quizzed on BBC Radio 4's Today programme about his suggestion that tectonic "plates" were shifting in the parliamentary party.
"What I was saying was some people perceived that was happening and therefore wanted to make statements.
'Not in Tony's mind'
"Tony Blair has been the most successful prime minister we have had,
everybody agrees that.
"Indeed, I can tell you for sure that if he decides, and I am sure he will,
that he wants to fight the next election, he would have the full support of the
Later at a press conference for the local and European elections on 10 June, Mr Prescott said there was "no doubt" in his mind about Mr Blair would carry on.
But he added: "I'm not in Tony's mind. He has to make the decision."
Mr Prescott said there was "no doubt" that if Tony Blair is leading Labour it will win the election.
"We believe the party support him, the public support him and he has been the
most successful prime minister this country has had for many years," he added.