Tony Blair is at the centre of speculation that he will resign as prime minister by the end of the year.
Mr Blair faces a test of his popularity in May's local elections
Downing Street aides quoted in the Daily Telegraph said Mr Blair would quit within nine months after rows over education reforms and loans to Labour.
But Local Government Minister David Miliband has said Mr Blair remains "strong" in office.
The prime minister has said he will go before the next general election but expects to serve a "full third term".
Transition of power
According to the Telegraph, Deputy Prime Minister John Prescott has tried to broker a deal between Mr Blair and backbenchers over his departure.
Standing in at prime minister's questions on Wednesday, Mr Prescott was asked when Mr Blair intended to resign.
He replied: "That is for me to know and you to guess."
Downing Street has denied reports in the Evening Standard that he will announce a detailed timetable for his departure at this year's Labour Party conference.
But some party activists fear Mr Blair's hand will be forced by May's local elections, which they fear will see the party lose control of a string of local authorities.
Mr Blair made the announcement that he would not seek a fourth term in Downing Street before the last general election.
He said at the time: "I would serve a full third term. I do not want to serve a fourth term - I don't think the British people would want a prime minister to go on that long. But I think it's sensible to make plain my intention now."
Mr Blair has since been beset by speculation about the timing of his departure, with many in the Labour party arguing for a smooth and "orderly" transition of power to Chancellor Gordon Brown.
Mr Blair said this week of his earlier announcement: "People kept asking me the question so I decided to answer it. Maybe that was a mistake."
But a Downing Street spokeswoman said Mr Blair had been cut off mid-sentence and had intended to say: "It was a mistake... to believe that the announcement would kill off the speculation as to when I would resign."
In recent weeks, the prime minister has been criticised over almost £14m in secret loans made to Labour before the last election.
He has also faced a battle with many of his own backbenchers over plans to give more independence to state schools in England, which some believe will mean a "backdoor" return to academic selection.
Labour MP Ashok Kumar, ministerial aide to International Development Secretary Hilary Benn, has written in an article that the prime minister should step aside "rapidly".
But Mr Miliband told the BBC: "I think we have got a very strong prime minister and an outstanding leader-in-waiting in Gordon Brown.
"I think that makes people like me, on the Labour side of politics, not just confident about the party's future but also about the country's future."