An ally of Ken Clarke has indicated he would back David Davis in a Conservative Party leadership fight.
Ken Clarke has taken soundings from party colleagues
Ian Taylor, who helped run Mr Clarke's leadership bids in 1997 and 2001, said Mr Davis could be the man to unite the left and right wings of the party.
Mr Clarke is thought to be considering a leadership bid after Michael Howard said he would step down.
The former chancellor is expected to reveal his plans during a series of television interviews on Sunday.
Mr Taylor, MP for Esher and Walton, said he would hold talks with Mr Clarke next week, but added: "David Davis could be the man for me.
"David has a strong base within the party on the right wing and that is the more dominant part of the party.
"Having been one of Ken's supporters in 1997 and 2001 I am trying to see if we could form some kind of coalition across the party, reaching out to the vast section of the population that seems to want to ignore us."
Another supporter of Mr Clarke, David Curry, said he believed he would be the best man to lead the Tories.
"The next Conservative leader will have to face Prime Minister Brown and perhaps in a situation where the economic situation is less comfortable for the government than it has been," the Skipton and Ripon MP told the Daily Mail newspaper.
"You have to ask who would be the best person to take on Brown in a real political maul and score points.
"As far as I am concerned there is only one man and that is Ken."
Mr Clarke has said he has been taking advice from colleagues about whether or not to stand.
He faces competition for the support of the party's left and modernisers from David Cameron.
Boris Johnson became the latest well-known Conservative to back Mr Cameron on Friday while Tim Yeo is also expected to offer his support in a television interview on Sunday.
Mr Davis remains the bookies' favourite, however.