He used a newspaper interview yesterday to declare: "I find it almost comic the number of people who tell me they would vote Tory if I were leader."
Today, Sir Malcolm Rifkind, the former foreign secretary, uses an interview with The Independent to make a coded attack on his leadership rival David Cameron, warning the Tories "not to lurch to Blairism".
The race for the leadership is accelerating with Mr Clarke expected to launch his candidature later this week and the front-runner, David Davis, due to make the first in a series of policy speeches after next weekend.
Mr Clarke spoke out in an interview with The Sunday Times as he won the backing of Tim Yeo, who abandoned his own leadership hopes to support the former chancellor. Mr Clarke told the paper: "I want to give this a bloody good go. The only job I want is Prime Minister."
He added: "Elections are fought in the centre. My strongest appeal is that I have higher approval ratings than any contender, higher still among wavering Labour and Liberal Democrats." Mr Clarke has been holding frequent meetings with senior aides planning the next steps in his campaign.
Mr Yeo said: "In my view, unquestionably the most likely person to defeat Labour and to see off the threat from the Liberal Democrats is Ken Clarke."
In his interview with The Independent, Sir Malcolm suggests that Tory "modernisers" are not firmly rooted in Conservatism and are trying to borrow from New Labour to reshape the party.
"There is no need to lurch to Blairism or the centre ground," he said. "I don't use the term moderniser because I start as a very convinced Tory. I do not feel any need to look to other non-Conservative ideologies for my political sustenance." Sir Malcolm also dismissed talk of a pact between Mr Clarke and Mr Cameron, and said "dream tickets" were often "dream nightmares".
He said he would not "rule out" an eventual deal with another candidate, but added it was unlikely: "I certainly don't want to be involved in that at the moment," he said. He pledged to loosen the power of whips if he became leader, and to give Tory MPs more freedom to vote according to personal views.
Another potential candidate, Liam Fox, the shadow Foreign Secretary, criticised the race as "the longest phoney war in history". He told BBC News 24: "It's still my intention to be part of that contest but we have got such a long wait that the Opposition should be concentrating on opposing the Government."
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