As the party faced the turmoil of a re-run selection contest forced on it by Lord Archer's resignation, speculation at Westminster centred on possible "big names" capable of taking on Labour next May.
Mrs Bottomley, the former secretary of state for health, and Mr Norman, the Asda millionaire and former chief executive of the party, refused to deny they were in the running.
However, Mr Norris, a former transport minister, remained the front-runner after he gave his strongest hint yet that he would stand. He was furious on Sunday when the party followed William Hague's instructions and decided to restart the race from scratch.
Yesterday, Mr Norris made clear that he wanted a "steer" from the leadership that his candidacy would be both approved and welcomed if he ran again. "I am coming increasingly of the view that my candidacy is indeed welcome in London. I have had the most enormous support from colleagues overnight."
Mr Norris was urged in a phone call yesterday by Mr Hague to run again, but the two men will discuss the matter further before making an announcement, probably today or tomorrow. Several shadow cabinet ministers, who believe their leader was wrong to re-run the contest, offered strong support in private to Mr Norris.
The former minister's well-publicised private life, dominated in recent years by revelations of five mistresses, could hinder him as the party strives for what one Tory MP called a "squeaky clean candidate".
Mr Norman, MP for Tunbridge Wells and shadow minister for Europe, is a close ally of Mr Hague and his application would be welcomed by Conservative Central Office.
As bookmakers William Hill installed him at odds of 8/1 as the next London mayor, and Mr Norris at 13/2, Mr Norman refused to rule himself out. "I am very flattered by the suggestion," he said. Yet Mr Norman's business background could create its own problems. Labour would highlight his paid directorship of Railtrack.
A cabinet ministerial source said Mr Norman would be placed in a difficult position because of his directorship of a firm that is in line to take a stake in the London Underground. The Government is ready to call for Mr Norman to resign his directorship or abandon his attempt to run for mayor, saying it would amount to a direct conflict of interests.
Similarly, Mrs Bottomley refused to deny rumours that she was preparing to stand. "I have lived in London all my life and I shall certainly be doing all I can to make sure our party chooses somebody who can represent our city with pride and distinction," she said.
Mrs Bottomley, MP for Surrey South West, has kept a low profile as a backbencher since the general election, but some senior Tories believe she would have a real chance of victory in the race.
However, the former Prime Minister John Major moved swiftly to scotch reports that he had any interest in standing. Mr Major's spokesman said: "If you recall, Mr Major was never in favour of there being a mayor of London at all. He is not a candidate for mayor. He cannot be persuaded to be a candidate for mayor. He will not be a candidate for mayor."
Other possible candidates who could be called on to stand include Iain Duncan Smith, the shadow defence secretary, who was approached last year by Central Office as a runner.
More realistically, Ivan Massow, the flamboyant chairman of the Institute of Contemporary Arts and self-made millionaire, will be called on again to stand. Mr Massow, who is openly gay, disappointed Mr Hague by pulling out of the race earlier this year. He said last night: "If I decide to go forward. I think I can offer the qualities of a youthful entrepreneur who doesn't carry any baggage. I come with a clean sheet."
Andrew Boff and Bob Blackman, both former Tory council leaders who made the shortlist from which Lord Archer was selected, are likely to run again. Eddie Lister, Lord Archer's deputy and the leader of Wandsworth council, may even run for the top slot himself.
All applications have to be submitted by 6 December, with the party's ballot due to end on 17 January. This timetable will still allow the Tories to have a candidate before Labour.
Former London transport minister; rose from humble Liverpool origins to become a millionaire car salesman.
Strengths: Street-smart, witty, came second in the previous ballot .
Weaknesses: Backs wholesale Tube privatisation (loved by Tories, hated by floating voters) yet also backs some form of congestion charging (hated by Tories and floating voters).
Sleaze factor: A "colourful" private life.
Former health secretary, described as "Golden Virginia" for her refusal to ban tobacco ads.
Strengths: Well-liked by many MPs and party members. As a woman could win crucial votes as the race to become the Tory candidate is likely to be dominated by men.
Weaknesses: Remembered chiefly in London for her plans to close many of the capital's hospitals, including Bart's.
Millionaire outgoing Asda boss and former Tory party chief executive.
Strengths: Close friend of William Hague, respected for business background.
Weaknesses: Loathed by many members and officials in London for his party reorganisation. Could be gaffe-prone.
Sleaze factor: Low, but Labour likely to highlight possible conflict of interest between his directorship of Railtrack and the award of contracts on the Tube.
Openly gay chairman of the Institute of Contemporary Arts. Made millions from business selling gay insurance.
Strengths: Liked and respected by Mr Hague, who wants to see his party as more open and inclusive. Self-made man with sharp wit.
Weaknesses: Not terribly well known among Conservatives in the capital. Would need to raise his profile.
Sleaze factor: Low.
Former Tory MP and one-time Heritage minister, now successful sport pundit. Heads football task force.
Strengths: High profile, popular figure, strong links with London.
Weaknesses: Had to resign in disgrace as "minister for fun" after revelations about his marital infidelities. Easily ridiculed.
Sleaze factor: He may have overcome his "roving eye" but is still associated with worst excesses of Conservative rule.Reuse content