Tory MPs are to vote on plans to change the way their leader is elected.
Mr Howard will stand down before Christmas
The proposals, which would give MPs the final say on replacing Michael Howard, have been agreed by senior backbenchers and the party's ruling board.
They require that candidates enlist the support of 5% of Tory MPs before being allowed to stand.
The proposals come as former chancellor Kenneth Clarke drops his strongest hint yet that he will make a third bid for the leadership of the party.
Meanwhile, 10 Tory MPs, including four leadership hopefuls, have criticised the election proposals in a letter to the Daily Telegraph, saying they deserve to be defeated.
Under the proposals, ordinary party members would only get their say on a candidate once he or she had secured the backing of 5% of Tory MPs.
Their views would be passed back to MPs, who would then hold a series of ballots to choose a leader.
Tory MPs, who have all been sent details of the proposals, along with ballot papers, are being asked to say whether or not they support them.
Voting begins at 1200 BST and will end at 1400 BST on Wednesday, with the result expected to be announced at a meeting of the 1922 Committee that evening.
If the vote comes out in favour, the plans will be drawn up into a formal amendment to the Conservative Party constitution.
MPs would then vote on them formally over the summer.
MPs appear divided over the proposals, with some, including potential leadership candidates Theresa May, Michael Ancram, David Willetts and Andrew Lansley, saying rank and file members should have a greater say, as they currently do.
The four, who were among the authors of the letter to the newspaper, say the party should promote devolution of power rather than centralisation.
Conservative members have already rejected Michael Howard's plan to allow party chairmen to rank candidates before a binding ballot of MPs.
Under the current rules, introduced when William Hague was leader, MPs choose two candidates to be put to a vote of all party members.
The only time it was used, Iain Duncan Smith was elected over ex-chancellor Ken Clarke.
In a speech to the Tory Reform Group on Tuesday evening, Mr Clarke, 65, will say the top job would be a "real privilege".
He has already suggested he has enough support from colleagues to mount a challenge.
"The more I consider my options, the prospect of my becoming a candidate by the autumn becomes more attractive," he will say.
It would be the third time Mr Clarke has tried for the leadership. In 1997, fellow MPs picked William Hague over him.
Mr Clarke's pro-Europe views might be seen as less of a stumbling block following the collapse of the EU constitution and no apparent prospect of British membership of the euro.
In his speech, Mr Clarke warns that the party "is in danger of becoming a natural party of opposition" and Gordon Brown - widely predicted to be the prime minister in waiting - "will not be easy to beat".
"We must look and sound like a credible government in waiting by the time we are campaigning against Brown in the second half of this Parliament," he will say.
Other likely candidates for a leadership contest expected in October include David Cameron David Davis, Sir Malcolm Rifkind, Liam Fox, Andrew Lansley and Kenneth Clarke. Transport spokesman Alan Duncan has ruled himself out of the race.