Ken Clarke has said he has enough support from fellow Tory MPs to compete for the leadership of the party.
Mr Clarke is pondering a leadership bid
Contenders are likely to need 20 nominations - 10% of Tory MPs - in order to stand in the election.
Mr Clarke, who has twice failed to become Tory leader, said he would make a final decision in the autumn.
Meanwhile, frontbencher David Willetts has said Britons are more like The Simpsons than Friends as he called for more support for families.
Mr Clarke, a former chancellor and home secretary, told LBC Radio: "The only job I want to do is to be prime minister...
"I've got the number of people I require to nominate me and I shall run unless it becomes clear by the autumn that I don't have a serious prospect."
Mr Clarke said he would not be willing to serve in the shadow cabinet under the leadership of any of the other potential candidates.
The precise rules for the leadership election, which is due to be held after the Tory autumn conference, are still being thrashed out.
Search for a partner
Shadow trade and industry secretary Mr Willetts continued his speeches about the future of Conservatism on Friday with a speech to the Child Poverty Action Group.
Mr Willetts pointed to family break-ups, referring to ex-Conservative chairman Lord Tebbit's famous speech about the unemployed.
He said: "Once upon a time we told people to get on their bike and went in search of work, so we shouldn't be surprised that some got on their bike and went in search of a new partner as well."
David Willetts compares Britons to The Simpsons
But most people still spent most of their time in households headed by a married couple, said Mr Willetts.
"Families and the vertical lines that link us across the generations remain very important," he argued.
"We might have a phase of our lives when we are living like an episode of Friends but most of us wind up like The Simpsons."
Mr Willetts, who has yet to say whether he will join the leadership race, said Chancellor Gordon Brown had helped the poorest in society but had not tackled "persistent poverty".
He said there was a "cycle of deprivation" where poor women have children in their teens then they do not do well and they were often concentrated in deprived estates.
"We need a radical change in the way in which social housing is allocated and housing developments are planned," he said.
Mr Willetts suggested the Conservatives had retreated from a "compelling vision" for Britain during the election campaign.
He added: "The retreat form bold visions may mark a deep uncertainty about our own country. We can't decide if Britain is a bad place to be or a good place.
"If we have a fuzzy and confused picture of our own country it is no surprise that our country has a fuzzy and confused picture of us."
Former Foreign Secretary Sir Malcolm Rifkind stepped up his leadership bid on Thursday, saying he expected to stand.
In an article in The Spectator, he said he had the required strengths to take on Mr Brown, thought most likely to the next Labour leader.