Tony Blair is reported to have given assurances to Gordon Brown that he will step aside to allow the chancellor to become premier.
Blair could quit two years into third term, reports claim
The pair have established a "working assumption" that would enable Mr Brown to take over the reins two years into the next Parliament if Labour wins the next general election, The Times claims.
It says Mr Brown has been assured that he is the only credible successor for the top job.
But the speculation flies in the face of Lord Falconer's insistence that Mr Blair is determined to be prime minister for a full third term and there was no plan for him to step down.
Last month, Lord Falconer, the Lord Chancellor, said: "Of course, no doubt at all about that. He will stand at the next election on the basis that he will stand for a whole term."
Also in July, the Mr Blair himself said his appetite for doing the job remained "undiminished".
But earlier this month Peter Mandleson, one of Mr Blair's closest allies, said he would not go "on and on and on and on" beyond the point where he was no longer wanted.
Reports of a pact between the prime minister and his chancellor are reminiscent of the infamous private meeting between the pair at the Granita restaurant in 1994.
As Westminster folklore goes, the supposed "deal" between the pair saw Mr Brown holding back from running for the Labour leadership following John Smith's death.
In return, Mr Blair was supposed to have agreed that he would at some stage stand down to make way for Mr Brown to become prime minister, reports the former has always denied.
According to The Times on Friday, the prime minister has reportedly indicated that he does not want to serve a full third term and was likely to resign after 10 years at Downing Street.
An unnamed minister reportedly told the paper: "The succession has basically, I think, been sorted out and making Gordon jumpy by pretending we want someone else to take over is in the interests of no-one.
"The government needs to get its show back on the road.
"Gordon and Tony need each other, otherwise there might not be a lot worth inheriting," the minister reportedly said.
Mr Blair and Mr Brown presented a united front in June when they shared a joint press conference aimed at talking up the benefits of euro membership and making the patriotic case for Britain's role in Europe.
A source reportedly told The Times: "There is no big dispute between Gordon and Tony on this any more."
A Downing Street spokesman told the BBC that he did not know where the succession story came from, stressing that the "prime minister is the prime minister".
It is widely believed that one of Mr Blair's first jobs when he returns from his summer break will be to try to shed the government's reputation for spin.
Alastair Campbell, the government's director of communications, is rumoured to be preparing to quit after the inquiry by Lord Hutton into the death of weapons expert Dr David Kelly.
Tom Kelly, one of Mr Blair's two official spokesmen, is facing calls to resign after he referred to Dr Kelly as a "Walter Mitty" character, a comment he later apologised for.
The prime minister's other spokesman Godric Smith is set to leave Downing Street in the near future.