Shadow home secretary Ann Widdecombe has confirmed she may throw her hat in the ring in the contest to succeed William Hague.
Miss Widdecombe said she would be taking soundings from colleagues to see if she can attract enough support to mount a successful leadership challenge.
She indicated that she would not reach a final decision until she had a chance to meet newly-elected Tory MPs after Parliament returns.
Miss Widdecombe - a right-wing, eurosceptic from the party's so-called "moral authoritarian" tendency - did however hold out an olive branch to the Conservative centre left.
She said that, if she became leader, she would be prepared to appoint pro-Europeans like ex-chancellor Kenneth Clarke to serve in her shadow cabinet.
"Every Conservative cabinet I can think of has included people from both wings of the party with a variety of views," she said.
"What you do need is a very clear party policy which everybody recognises is the policy and which is what you are offering to the electorate. Those two things are not incompatible.
"The Conservative Party has always been a broad church. You cannot just have a collection of Colonel Blimps."
Her conciliatory gesture comes amid increasing speculation that Mr Clarke could strike a pact in which he would agree to endorse shadow chancellor Michael Portillo as the candidate of the party's rival "social liberal" wing. Both Mr Clarke and Mr Portillo are spending the weekend considering their options.
According to reports, Mr Clarke is likely to declare his hand on Monday after addressing the centre left Tory Reform Group.