On Friday, John Baron and Rehman Chishti, little-known backbenchers, said they were considering a tilt at the leadership.
“I am being encouraged by my local team and others to put my name forward, and this I am now considering,” said Mr. Baron. “I would be a newcomer to the contest and do not yet have the required eight signatures, but will take soundings over the weekend.”
A senior party source said: “There will be a threshold so that candidates below that threshold will not be allowed to continue. We want to reduce the field to serious candidates and, if you can’t get a reasonable proportion of the party to support you, we don’t want grandstanders.”
The 1922 Committee of Tory backbenchers is meeting to decide the rules of the contest on Monday evening following an election of new members. The committee hopes to finish the first rounds of voting among MPs by July 21, when Parliament rises for its summer break.
Under the plans, any candidate with the support of more than 10 percent of MPs would take part in rounds of voting, with the candidate with the fewest votes being eliminated each time.
The threshold could even be raised to 15 percent, requiring potential contenders to have the support of 53 of their colleagues.
Other ideas under consideration include MPs taking part in two rounds of voting in a day, with a ballot in the morning and evening. But the Committee is expected to reject the suggestion of online voting in the contest amid fears it could undermine the secret ballot.