Footage of the veteran MP preparing for an interview was released by Sky News.
He said Andrea Leadsom had said some "extremely stupid things" and predicted Michael Gove would take the UK to war "with three countries at once".
He was talking to ex-foreign secretary Sir Malcolm Rifkind. Neither appeared to realise they were being recorded.
Mr Clarke, who has himself lost out when standing for Conservative leader three times, said he would probably end up supporting Home Secretary Theresa May.
He praised her but said she was a "bloody difficult woman", telling Sir Malcolm: "But you and I worked for Margaret Thatcher."
Turning to his assessment of Brexit campaigner and energy minister Mrs Leadsom, the Europhile Conservative MP said: "She's not one of the mindless, tiny band of lunatics, who think we can have a sort of glorious economic future outside the single market.
"So long as she understands that she is not to deliver on some of the extremely stupid things that she's been saying."
Justice Secretary Michael Gove is criticised by both men, with Sir Malcolm saying he does not mind who wins as long as Mr Gove is not in the final two.
Mr Clarke doubts Mr Gove would win the backing of Tory members, adding: "I think with Michael as prime minister we'd go to war with at least three countries at once."
But he did praise the justice secretary for ruining ex-London mayor Boris Johnson's leadership bid.
"He did us all a favour by getting rid of Boris. The idea of Boris as prime minister is ridiculous," Mr Clarke said.
The first round of voting is under way in the Conservative leadership contest, with Stephen Crabb and Liam Fox completing the lineup.
The party's 330 MPs have until 18:00 BST to cast their votes, with the results expected at about 19:00 BST, when the poorest performing candidate will be eliminated.
Ex-Conservative chancellor Ken Clarke has called the Tory leadership contest a "fiasco" and made disparaging remarks about the candidates.