Ex-chancellor Ken Clarke says he has "an excellent chance" of making it to the run-off for Conservative leader.
Fox, Clarke and Cameron all hope to make it to the run-off
Tory MPs vote on Tuesday, with the last of the four contenders eliminated. The top two in a ballot on Thursday will go through to a vote of all party members.
Mr Clarke told the BBC he was "the obvious person to pick" to increase the party's "appeal to the floating voter".
His campaign received a boost on Sunday when shadow health secretary Andrew Lansley said he would back him.
Mr Clarke and the other contenders, David Cameron, David Davis and Liam Fox, will make their final pitch to Tory MPs at a hustings on Monday.
Mr Davis has the public backing of 66, Mr Cameron of 33, Mr Clarke of 24 and Dr Fox of 19. About 50 Tory MPs have yet to declare how they will vote in the secret ballot.
If the MPs vote as they have declared Mr Davis would be guaranteed to make it to the run off - leaving the other three to battle for one spot.
Mr Clarke told BBC One's The Politics Show no one could predict how the voting would go, saying he believed he had enough support "to come first or second on Thursday".
He said he hoped the MPs would choose himself and Mr Cameron to contest the second stage of the leadership competition.
"He's probably too young and I'm probably too old. He's got no experience at all and I am loaded with experience. The ideal candidate may be somewhere between the two of us, half the age but half the experience. But he ain't there."
He said he was prime ministerial material now, and he thought Mr Cameron could be in the future, adding: "He (Mr Cameron) had one good speech and a fortnight's fantastic publicity, and timing is all in politics. But I think I'm going to thwart him."
Mr Lansley said he was backing Mr Clarke because "he has nothing to prove" and because he was the person the electorate had been saying for years they wanted to see as Conservative leader.