A think-tank boss who is a close ally of David Cameron is "the frontrunner" in the race to be the Tories' London mayoral candidate, says Oliver Letwin.
Nicholas Boles stood for the Conservatives in Hove last year
Mr Letwin, who is Tory policy chief, said Nicholas Boles, who runs Policy Exchange, was "absolutely admirable".
Outspoken DJ Nick Ferrari also says he would like to stand against current mayor Ken Livingstone in 2008, either as a Conservative or as an independent.
There are now five confirmed runners for the Tories' selection process.
Ordinary Londoners, not just Tory members, are to get a say on who the Conservative candidate should be in an X-factor style contest involving hustings and phone and text voting.
The candidates so far are Mr Boles, London Assembly Member Richard Barnes and James Cleverly, former parliamentary candidate.
Those are joined by Kensington and Chelsea councillors Victoria Borwick, Mr Norris's former running mate, and Warwick Lightfoot, a former government adviser.
With nominations due to close on Friday, critics say Mr Cameron's attempt to open up the race to people not normally known to be Conservatives has failed.
The party has reportedly been turned down by Michael Portillo and Lord Coe while Steve Norris, the candidate in the last two contests, has yet to decide whether to stand again.
In an interview with London's Evening Standard newspaper, Mr Letwin said: "To contest the mayoral contest requires 100% commitment; no one would underestimate the severity and ferocity of that challenge.
"A lot of people would think twice or thrice before putting their hats in the ring."
Asked if Mr Boles, 40, would have the profile and experience to mount a serious challenge to Ken Livingstone, he said: "He is the current frontrunner and I think he is absolutely admirable."
Police chief backing
Mr Boles failed to win back Hove for the Conservatives in last year's general election by just 420 votes.
Announcing that he was joining the primary contest, he said: "What matters is what Londoners want from their mayor, and what Conservative supporters in London want from a Tory mayoral candidate."
Among his rivals, former Metropolitan Police Commissioner Lord Stevens is acting as referee to Mr Barnes, according to the Evening Standard.
A Conservative spokeswoman insisted there had been "lots of interest" in the mayoral primary but the party would not reveal the number of applicants until nominations closed.
Mr Norris, who despite losing twice to Mr Livingstone was credited with running effective campaigns, told BBC Radio 4's PM: "I am absolutely clear that this is the best job in politics. Whether I will run myself is another matter."
He said voters might want "somebody younger and more exciting than a fat white, middle-aged, middle-class male".
But Mr Ferrari, a former Sun journalist who presents the breakfast show on commercial talk station LBC, said he had no such reservations.
Mr Ferrari says he is "good looking and virile"
"I would like to be mayor of London."
Asked if that would be as a Conservative mayor, he replied: "That's negotiable.
"I would be happy to take the Conservative ticket after some of the conversations I have had with David Cameron. I would be equally happy to do it on my own."
He added: "I think they [The Conservatives] want a winner. If you look at some of the bookies' odds I would appear to be a winner."
Asked about Mr Cameron's policy of trying to recruit more women and ethnic minority candidates, he said: "It is a question for the Conservative Party.
"Would they rather go for a white, slightly heavy, but nevertheless good-looking and virile radio presenter who can win?
"Or - purely for the sake of argument - a black woman from the East End of London, who nobody perhaps had heard of, who ticked all the right boxes but finishes fifth."