David Cameron has said he will not be Prime Minister beyond 2020 if he is re-elected for a second term in May, and has tipped George Osborne, Theresa May or Boris Johnson as potential successors.
He told the BBC that by the end of the decade “it will be time for new leadership” and compared serving a third term to a flaky breakfast cereal.
"Terms are like Shredded Wheat - two are wonderful but three might just be too many.”
His Chancellor, Home Secretary and the Mayor of London are “great people” with “plenty of talent”, Mr Cameron said, but did not say which one he would ultimately prefer to take over.
However in saying he does not wish to serve a third term, he risks being made to appear arrogant in the run up to the election in May, when he could be booted out after just one term of leading a Coalition government.
The Conservatives have not won a general election outright since 1992 and need to improve in the polls if they hope to end that streak.
In an interview with the BBC, Mr Cameron said the economy had “turned round” under his stewardship but said his job was only “half done” and that he wanted to “finish the job” of education and welfare reform.
But he added: "There definitely comes a time where a fresh pair of eyes and fresh leadership would be good, and the Conservative Party has got some great people coming up - the Theresa Mays, and the George Osbornes, and the Boris Johnsons.
"You know, there's plenty of talent there. I'm surrounded by very good people. I've said I'll stand for a full second term, but I think after that it will be time for new leadership."
Some believe that if Mr Cameron were re-elected in May, he would stand down as Prime Minister after keeping Britain in the EU after a planned referendum in 2017, handing over the reins to his successor, who would be ready to fight the 2020 general election as the new Conservative party leader.
A Labour spokesperson accused Mr Cameron of "taking the British public for granted".
"It is typically arrogant of David Cameron to presume a third Tory term in 2020 before the British public have been given the chance to have their say in this election," the spokesperson said. "In the UK it is for the British people and not the Prime Minister to decide who stays in power.
"Instead of focusing on themselves, it is time we had a Government focussed on the needs of working families. Another term of this Government would mean working people worse off and the NHS under threat because of their extreme spending plans. We need a better plan for a better future. We need a Labour government."