Ex-BBC director general Greg Dyke has said he considered running for London mayor but has decided against it.
Mr Dyke said he would only stand with Tory and Lib Dem backing
He revealed he had been approached by the Conservatives but would only consider standing as an independent with Lib Dem and Tory backing.
Mr Dyke said he liked "throwing ideas around" and that he wanted to "break the mould" in next year's election.
The Lib Dems say they turned down a Tory approach to field him as a joint candidate. The Tories confirmed this.
Mr Dyke said he thought he would lose to current mayor Ken Livingstone, who had done "not that bad a job".
He added: "I like throwing ideas around and my idea was 'can we break the mould of politics' and I think probably not."
Mr Dyke said the "only way" he could have won was to stand as an independent candidate with an agreement between the Tories and Lib Dems.
But he "hadn't agreed to do it", even if the parties had come to an arrangement, he added.
Mr Dyke, a former Labour supporter, resigned from the BBC in 2004, following the publication of the Hutton report into the death of weapons inspector Dr David Kelly.
He is an opponent of the Iraq war and has been outspoken about his treatment by Labour ministers.
Lib Dem chief of staff Ed Davey said the Tory proposal had been "very odd", and may have been against the party's rules.
He said Mr Cameron had proposed the idea of a joint candidate to face Mr Livingstone in a meeting with Lib Dem leader Sir Menzies Campbell on Wednesday.
Mr Davey said: "The people of London should have a full democratic choice on next year's mayoral elections. David Cameron's proposal would have denied that."
He added: "There are many problems with Ken Livingstone's performance as mayor, but the way to defeat him is not to have an 'anyone-but-Ken' candidate, it is to win the argument over issues that matter to the capital.
"London is increasingly a liberal city and the people of London deserve a liberal choice for mayor."
But he told Sky News: "If Greg Dyke wants to be the Liberal Democrat candidate and puts himself forward, I'm sure he stands a very good chance of getting himself elected."
Conservative chairman Francis Maude said: "David Cameron had discussions with Greg Dyke, starting at the end of last year, about the prospect of becoming a candidate for mayor of London.
"These discussions included the possibility of there being a joint Conservative-Lib Dem candidate.
"Throughout this, our aim has been to get the maximum number of good candidates to stand to give London a real choice.
"However, Ming Campbell said that he was not allowed to go ahead with any form of joint candidate, irrespective of the merits of the candidate, because of their constitution.
"In any event, Conservative Party members in London would have been given a say in the process."
Mr Maude said more than 40 people had already applied to take part in its "open primary".
The party has said the winner will be "well known" by the end of the process, which it has compared to the TV talent show X-factor.
The Conservatives have reportedly been turned down by several potential high-profile candidates including London Olympics supremo Lord Coe, radio presenter Nick Ferrari and former Metropolitan Police chief Lord Stevens.