He will declare his support for the shadow Foreign Secretary, Liam Fox - the most right-wing of the five declared leadership candidates - on the Jonathan Dimbleby programme today.
Mr Wheeler, who donated £5m to the Tories' 2001 election campaign, shares Dr Fox's strict views on marriage. In an interview in August he said that "unmarried mothers get protected too much". Dr Fox has said during the campaign that he wants to use tax breaks to encourage couples to marry, and he wants more restrictive abortion laws.
The right-wing Cornerstone Group, which claims the support of up to two dozen Tory MPs, is also weighing up whether to support Dr Fox or put up a sixth candidate who shares its mix of anti-EU nationalism and social conservatism. One possible choice would be the current deputy leader, Michael Ancram, who is deciding whether to run.
Rising support for Liam Fox has presented middle-of-the-road Conservatives with what they regard as a nightmarish prospect: that when party members are balloted later in the year, the choice will be either Dr Fox or the frontrunner, David Davis - both from the party's right wing.
Allies of Ken Clarke fear that the long shadow of Margaret Thatcher could frustrate him again in his third attempt to win the party leadership.
He hopes to persuade party members that he is the only candidate who can fight Tony Blair on what is traditionally Labour's home ground. In an article for today's Independent on Sunday, he attacks the way Labour has run the NHS, creating a "culture of centralism". But before he can put his case to party members, he has to secure the backing of enough Tory MPs to win himself a place on the ballot paper.
A lavishly illustrated book of tributes to Lady Thatcher, with contributors ranging from the former Soviet president Mikhail Gorbachev to the former deputy prime minister Lord Howe, will be published this week, ahead of her 80th birthday on 13 October. Mr Clarke's supporters fear that Baroness Thatcher will use the limelight to try to persuade Tory MPs to reject him.
John Bercow, who was a prominent Thatcherite in the 1980s but is now backing Mr Clarke, implied that it would be better for the party if Lady Thatcher kept quiet. "I continue to admire Lady Thatcher enormously, but I don't think any intervention from her would be or should be of any special significance."
But John Hayes, a leading member of the Cornerstone Group which campaigns to keep Thatcherism as the party's prevailing ideology, said: "Most people value Lady Thatcher's opinion and what she says will be regarded with the respect it deserves."
The baroness's intervention in the last two Tory party leadership elections helped the eventual winner to defeat Mr Clarke, whom she has never forgiven for being the first cabinet minister to tell her to her face that she should resign. In 1997 she backed William Hague, and in 2001 she pointedly withheld her support from Michael Portillo.
The five declared candidates in the race - Ken Clarke, David Davis, Liam Fox, David Cameron and Sir Malcolm Rifkind - will take part in a "beauty contest" at the Conservative Party conference which starts in Blackpool tomorrow, when each will have the opportunity to make a set-piece speech from the stage.
On Tuesday week, MPs will start the first of a series of ballots that will reduce the number of candidates to two. David Davis, who has the declared support of 56 MPs, is virtually guaranteed a place in the final run-off. Mr Cameron is on the party's right, but is vulnerable to attack because of his background. He is an Old Etonian, and his wife, Samantha, is a baronet's daughter.Reuse content