Shadow home secretary Ms Ann Widdecombe has confirmed she may throw her hat in the ring in the contest to succeed Mr William Hague.
Ms Widdecombe told The Sunday Telegraphshe will be taking soundings from colleagues to see if she can attract enough support to mount a successful leadership challenge.
She indicated that she will not reach a final decision until she has had a chance to meet newly-elected Tory MPs after Parliament returns.
Ms 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 will be prepared to appoint pro-Europeans like ex-chancellor Mr 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 told the paper.
"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 Mr 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 The Sunday Telegraph, Mr Clarke is likely to declare his hand on tomorrow after addressing the centre left Tory Reform Group.
PA