Mr Dorrell's colleagues moved to dampen the speculation, along with rumours that half a dozen present and former cabinet ministers are gathering campaign teams around them for the contest.
Meanwhile, reports that the Secretary of State for Health is planning sweeping changes were in part confirmed by the news that a forthcoming White Paper will look at ways of taking welfare out of the public sector.
Labour's campaign manager, Brian Wilson, said the proposal was evidence of infighting in the Conservative Party.
Mr Dorrell was on a mission to demonstrate that "contrary to appearances, the blue blood of Thatcherism is running through his veins," he said.
Mr Wilson added: "It has been another frenetic weekend of jockeying for position from the Tory frontrunners. This is the election campaign they are preoccupied with fighting."
He added that other Conservative leadership camps had been briefing journalists on tough questions that they could pose to their rival, Michael Howard, the Home Secretary.
Mr Howard was adamant, however, that no such contest was going on. Interviewed on BBC television, he rejected suggestions that he was one of a group of ministers already campaigning for the succession which is bound to take place if the Conservatives lose the election.
Five other possible contenders have been named over the weekend. They are Michael Portillo, the Defence Secretary, John Redwood, former Welsh Secretary, Michael Heseltine, deputy Prime Minister, Malcolm Rifkind, Foreign Secretary, and Ian Lang, President of the Board of Trade.
Mr Howard said: "Let me make it absolutely plain. There is only one campaign that I want to win and that is the campaign to win this general election. I hope that John Major will remain Prime Minister for a very long time."
Meanwhile the Health Minister, Gerry Malone, confirmed that there would be a White Paper on the social services in March, but would not say whether it would involve compulsory competitive tendering for welfare programmes.
However, he did say that existing projects involving private and voluntary providers had worked well: "It is a highly successful principle that this government has put into place. It would be ludicrous to suggest that we should not be looking for opportunities in all sorts of policy areas to expand it where it is sensible to do so."
Labour's spokesman for health issues, Chris Smith, said: "The private sector does have a role to play and it is doing so up and down the country. But what isn't needed is a diktat from Whitehall saying that directors of social services have to put out every service that they provide to competition."Reuse content