Some candidates in the Conservative leadership contest should consider pulling out, Housing Minister James Brokenshire will say later.
The communities secretary is not standing for the role but says the party needs to find a new leader fast.
Theresa May steps down on Friday and 13 Conservative MPs so far have put themselves forward to succeed her.
Mr Brokenshire will call on the least popular candidates to retire before nominations close next week.
Currently, MPs only require the backing of two parliamentary colleagues to stand in the leadership race.
Senior Conservatives will meet on Monday afternoon to discuss whether to change the rules so potential candidates need more supporters to begin their bid.
A final decision will be made by the executive of the backbench 1922 Committee on Tuesday.
After nominations close, all 313 Conservative MPs will vote for their preferred candidate in a series of polls that will whittle down the contenders one by one.
Some MPs are keen to reduce the number of hopefuls swiftly, since the wider Tory membership of 124,000 will only vote on two candidates.
“We simply do not have the luxury of weeks of navel gazing or days and days of whittling candidates down to the final two and talking to ourselves,” Mr Brokenshire is expected to say in a speech to the centre-right think tank, Policy Exchange.
Mr Brokenshire will also use the speech to suggest people should be allowed to use part of their pension pot to help them buy their first home.
“To those who are in their 20s and finding it difficult to save, this idea offers a genuine route to a deposit,” he is expected to say.
The suggestion is a “personal idea any leadership contender should consider seriously” he says.
Who will replace Theresa May?
The winner of the contest to lead the Conservative Party will become the next prime minister.