Conservatives can opt for a "one nation" candidate or a right-winger in choosing a new party leader, Sir Malcolm Rifkind has said.
Sir Malcolm was foreign secretary under John Major
If they want a more moderate leader then he would be interested in the job, the former foreign secretary said.
Meanwhile, potential rival Liam Fox said that, by announcing his intention to quit early, Michael Howard sparked "the longest phoney war in history".
And Tim Yeo has pulled out of the race, backing ex-chancellor Ken Clarke.
In an interview on BBC Radio 4's Today programme Sir Malcolm was asked if he was intending to offer an alternative to bookies' favourite David Davis.
"If the Conservative Party wants to choose the one nation tradition of Conservatism as the way in which it will regain the confidence and support of the public, then I would be proud to be its leader," he replied.
"If the party, in its wisdom, comes to the view that a more right wing policy concentrating on immigration, on Europe and issues of that kind are the way forward then obviously it should look elsewhere.
"I think that's a real choice and I think it's important that in appealing to the public, the party should first be clear what its own priorities are".
Dr Fox meanwhile urged the party to concentrate on attacking the government instead of indulging in "endless speculation" about its future.
The party foreign affairs spokesman said it was vital that Conservatives spelled out their vision for the country.
Dr Fox, speaking on the BBC News 24 on Sunday programme, said: "This is the longest phoney war in history.
"It's still my intention to be part of that leadership contest whenever it comes, but we have got such a long wait for it that the opposition should be concentrating on opposing the government rather than involving themselves in endless speculation.
"What the country requires is a clear political agenda.
"If we simply adopt the sort of approach we had in recent years and say what is it that voters want to hear and then tell them it, that's not the sort of politics most of us want.
"The Conservative Party's biggest problem is it seems to want to talk about the Conservative Party far too much."
Dr Fox said politics had become a "glorified, second rate soap opera" with personalities and image more important than policies.
He said: "Politicians need to stop talking about themselves, their alliances, their friends and their party and start talking about what's good for the country."
The leadership contest, which has not officially begun, started after the general election when Mr Howard announced he was standing down after Labour's third victory.
He will quit by the end of the year.
Other candidates include David Cameron, David Willetts, Theresa May and Andrew Lansley.