Former foreign secretary Sir Malcolm Rifkind says it is "quite likely" he will stand for the Tory leadership.
Sir Malcolm says people will have to be patient about his decision
"I think it is foolish to pretend that one is not interested," the shadow work and pensions secretary told the BBC.
He was speaking ahead of a speech in which he said it was "not an option, but a necessity" for the party to win back the centre ground.
Michael Howard says he will step down as Tory leader by Christmas after the party failed to win the election.
He did not quit immediately because he wanted the rules governing the selection of a leader to be changed first.
Although there is no open contest yet, a number of Conservative MPs are seen to be jockeying for position.
Among those thought to be considering standing are Kenneth Clarke, David Davis, Liam Fox, Alan Duncan, Tim Yeo and David Cameron.
Sir Malcolm said that people will have to be "a little bit patient for a little bit longer" about his final decision on whether to stand or not.
But he rejected suggestions that his background as a member of the Thatcher and Major governments would make him unacceptable to many of the middle-ground voters he hopes to attract back to the party.
While the Thatcher administration had "made some serious mistakes", such as the introduction of the poll tax "it was one of the most impressive governments of post-war years, and I'm proud to have been a part of that," he said.
In a speech to Conservative Mainstream, a think-tank which promotes modernisation of the party, Sir Malcolm urged members to turn their attention away from leadership speculation and towards how to improve its election prospects.
Whether the next leader should be in his or her 30s, 40s or 50s, or whether it will help if they were state school or public school educated were "subjects of endless fascination", he said.
"But unless we can rise above them we are wasting our time."
TORY LEADERSHIP RUNNERS AND RIDERS:
Sir Malcolm Rifkind
People would, however, "be very interested in what the Conservative Party is saying about the future of our country, about our ideas, our policies and our aspirations", he said.
"In 2001, the public had the impression that we were pre-occupied with Europe - in the recent general election they felt we were pre-occupied with immigration and asylum," he said.
"These were real issues that needed to be addressed and we had much to say on health, education and other matters, but the public were not convinced that we were yet ready for government."
'Britain of our dreams'
Sir Malcolm said: "The reality is that winning back the centre ground is not an option, but a necessity for the Conservative Party."
He spoke of a "Britain of our dreams", where civil liberties are defended, and the state "is not the enemy of freedom but restricts itself to its proper concerns of administering justice and punishing the lawbreaker".
Asked by BBC Five Live if he was "a bit posh" to be making his appeal, Sir Malcolm said: "I'm not posh in the slightest - I grew up in a tenement building from a middle class family like millions of other people. What do you mean posh?"
His speech came as Tory MP Damian Green refused to rule himself out of the leadership race, but expressed his delight that One Nation Conservatism was back in fashion.
Mr Yeo said there was "no rush" for any MP to decide whether they should stand.
Shadow transport secretary Alan Duncan is expected to make a speech later this week outlining how he thinks the party can improve itself.