By Terry Stiastny
BBC political correspondent
After eight years in opposition, former minister Tim Yeo says the Conservatives need a leader to beat Labour and see off the Liberal Democrats. He believes Ken Clarke is the man for the job.
Kenneth Clarke: One of the most charismatic Tories
So Tim Yeo has withdrawn from a leadership race which has started in all but name in order to support the former chancellor.
Mr Yeo says Ken Clarke has the experience in government - and particularly in handling the economy - which would allow him to present the best challenge to Labour at the next election.
He also believes Mr Clarke would be able to provide an element of popular appeal outside the party's core supporters.
"Crucially he has the strongest appeal to people who do not currently vote Conservative - the very voters whose support we must regain if we are to win the next election," said Mr Yeo.
But others are more sceptical about Mr Clarke's suitability for the leadership this time round. They believe that several factors could count against him.
Among them are his age - he could be approaching 70 by the time of the next general election - his position on the liberal wing of the party, and in particular his pro-Europeanism.
Some say Mr Clarke is too relaxed towards his political life
Ken Clarke recently said he no longer believed joining the Euro would be right for Britain. His supporters argue Europe won't be as crucial an issue for the Conservatives, and the country, as it has been in recent years.
Shadow foreign secretary Liam Fox - himself a potential leadership candidate - said he welcomed anyone who accepted the logic of a more Eurosceptic case.
But he believed the Conservatives should still be concentrating more on their policies than on personalities, and that the country required a clear political agenda - a veiled criticism of Mr Clarke.
If he ran, it would also be the third time Ken Clarke had tried to become Tory leader. He lost in both 1997 and 2001.
Since it became obvious there would be a vacancy, he has publicly weighed up his options, saying at one point that he didn't like to make a habit of losing in those contests.
If he does enter this race, he'll join a list of contenders which is also likely to include David Davis and David Cameron, as well as the former foreign secretary Malcolm Rifkind.
Ken Clarke was spotted watching England play Australia at the Ashes on Sunday afternoon - he seemed to be concentrating more on the cricket than on politics.
To his supporters, that's the kind of moment which shows Ken Clarke is in tune with the public mood, and which would make him a strong challenger to Tony Blair or Gordon Brown.
His detractors might see it as the mark of a man who takes too relaxed an approach to his political life.
To outsiders, the rules of Conservative leadership elections sometimes seem as arcane as cricket does to those who don't follow the sport.
But the entry of one of the biggest personalities in Conservative politics to the campaign would no doubt help to make for a lively contest - perhaps even one as closely fought and as avidly followed as this cricket series.