The former Chancellor has told friends that the odds are strongly against him succeeding John Major and that William Hague is almost certain to win.
Mr Clarke has all but ruled out serving in a Eurosceptic Shadow Cabinet under Mr Hague. Hefaces having to return to the back benches, but is said to be sanguine about his fate.
Peter Lilley, the former Social Security Secretary, who threw his weight behind Mr Hague last week after coming second to last in the first ballot, is in line to become Shadow Chancellor. Michael Howard could become Shadow Foreign Secretary.
Sources close to Mr Hague described as "speculation" suggestions that Mr Clarke might be offered the job of deputy leader, adding that Mr Hague would want all the leadership contenders in his Shadow Cabinet if they accepted his policies.
But David Curry, Mr Clarke's campaign manager, said that if the former Chancellor loses the election he would only be willing to work in a Shadow Cabinet which does not apply "an ideological test" on Europe. "What concerns us is the apparent intention of Mr Hague to exclude from his Shadow Cabinet anyone whose views on Europe or the single currency are different to his," he said. "That would be a terribly divisive way to address the party. It would be the opposite of uniting. Ken wants to unite it."
If Mr Clarke is excluded from a Hague Shadow Cabinet, other centre- left big hitters, including Michael Heseltine, may also retire to the back benches.
Some Clarke supporters believe he could best lead the left from the back benches, rather than soldiering on in a Shadow Cabinet in which he did not believe, performing a job for which he was not overly-enthusiastic.
Mr Hague said in a letter to Tory MEP Caroline Jackson that he "would expect every shadow minister" to support his policy of ruling out a single European currency for at least 10 years. This shatters Mr Clarke's "wait and see" compromise on which the Tories fought the election.
Mr Curry said: "There is no point in writing the manifesto for 2002 now. The leadership election is not a referendum on Europe.
"If we are going to turn it into [one] particularly when the situation in Europe is changing dramatically as we look at it, that would be a terrible mistake. Ken is saying it is idiotic to say that everyone has to have an identical view on Europe."
The 164 Conservative MPs will vote in the second ballot on Tuesday. Mr Clarke, who won 49 votes in the first round, could poll around 60. Mr Hague, who won 41, is expected to pick up around 20 more, while third- placed John Redwood faces elimination. Unless Mr Clarke concedes, a third and final ballot between him and Mr Hague will take place on Thursday.
Mr Clarke's supporters yesterday said that they are hoping to exploit the bitterness between the Redwood and Hague teams. Mr Redwood's supporters are furious that Mr Lilley and Mr Howard refused to back their candidate, instead preferring Mr Hague, who is distrusted by many on the right.
One Clarke backer said: "There is so much vitriol between the Redwood and the Hague camps that I would be stunned if Redwood could bring himself to endorse Hague in the final ballot. Endorsing Clarke would be the mature thing to do."
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