Kenneth Clarke says he would like to lead the Tories but won't decide for about 10 days on whether to stand as a candidate.
He said he had to consider whether he could lead a party which had just carried out a eurosceptic election campaign.
Other senior Tories are considering whether to stand against Michael Portillo for the right to succeed William Hague.
Mr Clarke said: "I'm not going to decide (about whether to bid for the leadership) for about 10 days or so.
"There's no need for candidates to decide until then. I'm going to carry out more soundings among my friends and parliamentary colleagues.
"I would like to be leader of the Conservative Party and I have not given up my ambition yet to one day be Prime Minister.
"I have to decide whether a parliamentary party that has just fought a frenetic eurosceptic campaign is really capable of being led by a pro-European.
"That requires some careful consideration with many members of the parliamentary party."
Yesterday shadow chancellor Mr Portillo became the first confirmed candidate and shortly afterwards shadow defence secretary Iain Duncan Smith said he was thinking about challenging.
Ann Widdecombe had already indicated she is contemplating a leadership bid.