The former chancellor is expected to make a formal statement in the next two weeks, confirming that he is going to make another attempt for the top job that has twice eluded him without waiting to find out what the rules of the contest will be this time.
Previously, it had been thought that Mr Clarke would hold back until 27 September, when the issue of who chooses the next Conservative leader will have been decided.
Mr Clarke, who is in his Rushcliffe constituency this weekend, was in his Westminster office last week taking soundings about his political future.
A friend said: "He has come through the summer thinking that he finds the job increasingly attractive. If you want the big job you go through the process in the circumstances as they stand." According to The Sunday Telegraph, the Clarke camp said: "Ken can win with or without David Cameron."
Conservative Party officers are being balloted on whether they agree that Tory MPs alone should choose their leader. This was the system that operated from 1964 to 2001, and was used to elect every party leader from Edward Heath to William Hague.
It is assumed that Mr Clarke has a better chance of winning if the Tories revert to the pre-2001 system, than if the final decision goes to a ballot of the whole party membership. In the one election in which members had the vote, Mr Clarke was decisively beaten by Iain Duncan Smith, who was ousted two years later by his fellow MPs.
His decision coincides with a bid by right-wing MPs to convince the party to head off rule changes planned by Michael Howard.
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