The former prime minister said that the team would be more impressive than that of the Government and said he hoped it may mark "a moment when the terms of political trade begin to change".
As Mr Cameron and Mr Davis continue their countrywide campaigns to woo Tory members before the final leadership ballot, Sir John gave a clear hint he is backing David Cameron. The former leader said: "I live in hope that when we have selected one of the two Davids, that we'll have a Shadow Cabinet that includes Ken Clarke, Malcolm Rifkind, William Hague, David Davis, Liam Fox."
Mr Clarke has refused to serve in the Shadow Cabinet since the Tories lost office in 1997, and he would have to forego more than £250,000 a year in director's fees if he returned full-time to the Shadow Cabinet. However, Mr Clarke said last week he would consider serving as a shadow Foreign Secretary or shadow Chancellor. He told the BBC at the weekend he would consider a frontbench job "if I thought it was a more attractive proposition than doing my elder statesman stuff from the back benches where I gave the Government a lot of trouble."
Mr Hague, widely regarded as one of the ablest politicians at Westminster, would also enhance the Tory front bench.
Sir John admitted for the first time he had made a mistake in not taking on the Eurosceptics, whom he once described in private as "the bastards", when he was Prime Minister.
"It did go too right-wing for my taste. I didn't like it, I wasn't comfortable with it," he said on BBC1's Sunday AM. "I'm getting much more comfortable by the day and, from what I hear going around the constituencies, that is true of many, many, many other people. I think it's a very attractive direction in which we're now headed."
Mr Davis made it clear in an interview for today's Independent that, although he disagreed with Mr Cameron over policy, he could work with his younger rival. He said they had worked together closely in preparing Sir John for Prime Minister's Questions.
"I don't have a poor view of David Cameron," he said. "I worked with him. We had these 7am meetings preparing questions for John Major's PMQs. All I can remember is the laughter."
Mr Davis is planning to outflank Mr Cameron with plans for big tax reductions paid for by cutting public spending below economic growth over three years. One option is to reverse the £5bn cut in tax by Gordon Brown on pension funds.
Mr Davis spoke for the first time about his poorly received Tory party conference speech for which he blamed himself. He said the media were out to "bring down the front-runner". Although he denied he was paranoid about the media, there is growing anger in the Davis camp at a "dirty tricks" campaign.
Yesterday Derek Conway, MP for Old Bexley and Sidcup and an important ally of Mr Davis, attacked the BBC for being biased in favour of Mr Cameron. He told GMTV: "I think the BBC have decided who they want to lead the Tory party."
On Friday, Mr Davis ordered aides to make a formal complaint against the BBC after discovering that the PM radio programme was preparing a report alleging he had broken a promise not to answer questions about drugs during a visit to Warwick University.Reuse content