This comes after FBI agents searched his Mar-a-Lago home as part of an unrelated federal probe
The Conservative Party committee overseeing the contest to select British Prime Minister Boris Johnson's replacement will look to whittle it down to two names by July 20, one of its members said on Saturday.
The so-called 1922 Committee will set out the exact rules and timetable for the contest next week after Johnson was forced to quit by his own party. Many lawmakers are pushing for a fast-tracked process.
Four Conservative lawmakers have officially confirmed their desire to be the next leader, but about a dozen others are also expected to run for the job.
Conservative lawmakers will hold a series of votes to reduce the field to two final candidates, who will then face a postal ballot of the wider Conservative Party membership.
"Clearly what we would want to do, and I think even the candidates would admit this is, is to eliminate some of those that are clearly not going to get enough support to get in the last two at a relatively early stage," 1922 Committee treasurer Geoffrey Clifton-Brown told Times Radio.
Clifton-Brown said this could be done by upping the number of signatures from other Conservative lawmakers required to be nominated, and by increasing the threshold of votes candidates must receive to progress to the next round.
"I think that we will be able to frame a process to actually come up with two names by the time parliament goes down on the 20th of July," he said. "We should have an answer by the time of the party conference in October and maybe before that."
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