The Conservatives have set out a five-month timetable to choose their candidate for London mayor.
Mr Cameron suggested a Greg Dyke candidacy to the Lib Dems
The party will shortlist applicants, who then go to an "open primary", with all Londoners on the electoral roll allowed to vote in the contest.
The winner will be announced at the Tory conference in September.
The announcement follows the revelation that ex-BBC director-general has ruled out standing as a Conservative-backed candidate in next year's mayoral race.
The deadline for applications is 16 July, with a short list drawn up by 3 August.
Following a series of hustings, the primary will be held, closing on 26 September.
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.
Chairman Francis Maude, said: "This timetable is the beginning of the end of Ken Livingstone's London reign.
"For the first time, any Londoner on the electoral roll will be able to take part in choosing the candidate of a major political party."
The Conservatives had sought to select their mayoral candidate last year but decided to delay the process after failing to unearth a suitably high profile candidate.
Possible candidates have included Lord Coe, radio presenter Nick Ferrari and former Metropolitan Police chief Lord Stevens.
Mr Dyke said he had been approached by the Conservatives but would only consider standing as an independent with Lib Dem and Tory backing.
Tory leader David Cameron discussed the idea with Lib Dem counterpart Sir Menzies Campbell but it was dropped.
Mr Dyke said he thought he would lose to Mr 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."
Lib Dem chief of staff Ed Davey said the Tory proposal had been "very odd", and may have been against the party's rules.
Mr Maude said that, even if the plan involving Mr Dyke had gone further, "members in London would have been given a say in the process".
He added that more than 40 people had already applied to take part in the Tory primary.