Cabinet ministers will try to persuade David Cameron to commit to U-turn on his decision to quit as Prime Minister before the next general election.
The Conservative leader announced a year ago that he would not seek a third term in office, but has repeatedly refused to set out a timetable for his departure.
Speculation has been flowing over who might replace him ever since last May’s election victory for the Conservatives, but a number of senior figures within the party want Mr Cameron to stay on for the 2020 contest.
One said: “It is by no means a sure thing that he will go before the election. He can be persuaded. It would give others a chance to come through.”
Home Secretary, Theresa May, Chancellor George Osborne and Boris Johnson, the Eurosceptic Mayor of London and Tory MP, are among those tipped to run to replace Mr Cameron.
Mr Osborne’s chances suffered a blow after his Budget was roundly criticised as multiple U-turns were performed, including one on controversial changes to disability payments.
There has also been speculation that Stephen Crabb, who last week replaced Ian Duncan Smith as Work and Pensions Secretary, could be an outside contender for the position.
If the Prime Minister – who compared terms in office to Shredded Wheat breakfast cereal by saying: “Two are wonderful but three might just be too many” – was to delay his departure, it could help a surprise candidate such as Mr Crabb.
Ministers also believe the PM is a unifying figure within the Conservatives, despite the party being publicly divided over Europe.
One said: “He’s got the backing of most MPs.
“There are those who hate him, but it is a small group. He is doing a good job, it is a very difficult job, and he is great in a crisis.”
A YouGov poll for in January indicated that 55% of Tory voters want Mr Cameron to delay his departure until just before the 2020 election at the earliest.
Of those, 22% want him to break his vow and seek to serve a third term. Only 15% of Tory voters are urging him to leave office before 2019.
Among the wider electorate, 37% of voters want Mr Cameron to remain as leader until the 2020 election. 11% would like him to stay longer. Only 32% want him to stand down before 2019.