Front-runner in the Tory leadership race David Davis has said he has not yet decided whether to run for the job.
Mr Davis' profile has risen significantly during his shadow home secretary role
The shadow home secretary did not rule himself out of the contest, but said he always made his mind up about "these things at the last possible minute".
His comments come as former Chancellor Ken Clarke is said to be "anguishing" over whether to stand for the post.
The party's board meets on Monday to start debating changes to the rules governing its leadership contest.
Many in the party believe the last say on who leads the party should be given back to MPs who understand what qualities are required.
But former party leader Iain Duncan Smith has called for more respect to be shown to the party's grass roots.
A number of senior Tories cited Mr Duncan Smith's election as leader in 2001 as an example of activists being unrepresentative of public opinion.
A survey for BBC Radio 4's Today Programme found that most Tory constituency party chairmen who responded wanted MPs to choose Michael Howard's successor.
Party members currently vote for its leader from a shortlist of two chosen by MPs.
Speaking on BBC One's Breakfast with Frost, Mr Davis, who is 13/8 favourite with bookmakers William Hill, would not say whether he planned to stand for the leadership.
"We are talking about something that is six or seven months away at the earliest.
"My concern at the moment is that we learn the lessons from the last election and make sure that we're the next government."
But he added: "I made my decision not to run last time a few days before it happened and I'll make my decision very clear when the day comes."
One of the Tory party's leading fund raisers and president of the Dixons group Lord Kalms has thrown his weight behind Mr Davis.
On Saturday, former Deputy Prime Minister Michael Heseltine said he believed Mr Clarke was the best qualified person for the role.
But he warned that although he thought the public found Mr Clarke approachable, that winning the leadership contest would prove a "very, very difficult battle".
Former party leader William Hague, who is second favourite to Mr Davis with bookmakers William Hill to take over, has said he would not stand.
And last week the new 33-year-old Shadow Chancellor George Osborne ruled himself out of the race, prompting backing for another young rising star Shadow Education Secretary David Cameron - who is now third favourite.
Shadow Foreign Secretary Dr Liam Fox and Shadow Work and Pensions Secretary Sir Malcolm Rifkind are also potential candidates.