Senior Conservatives are to vote on whether to make it easier to force Theresa May out of office within weeks by changing the party’s rules to allow a no-confidence motion at any time.

The 1922 Committee will meet later on Tuesday to discuss amending its rules, which currently state a leader cannot face a second no-confidence motion within a year of the previous one.

May defeated an attempt to oust her in December, meaning she is safe from an official challenge for at least another seven months.

However, some Brexit-supporting members of the committee are trying to remove the time limit.

There is a suggestion it could be shortened to six months, meaning she could face a contest in June. But one senior committee officer said there would be an attempt to remove the time limit altogether, as there was an appetite to get on with removing May as soon as possible.

If the rules are changed, at least 15% of Conservative MPs – 47 of them – would need to send letters to Sir Graham Brady, the chair of the committee, in order to trigger another confidence vote. This threshold is likely to have already been met, given the scale of discontent within the parliamentary party.

The officer said opinion on the committee was “finely balanced” as there were roughly equal numbers of remainers and Brexiters, but feeling was “building up against May” because of the Conservatives’ dire poll numbers.

They said the preference would be for May to listen to Brady’s message to her that large numbers of MPs and members are unhappy with her premiership, and set out a timetable for her departure of her own accord.

In contrast, another committee source said no decisions had been made, and most of the reports about attempts to remove May “have only reflected the views of one or two members”.

A couple of the 20 members of the committee have already spoken openly of their desire to get rid of May. Nigel Evans, the committee’s joint executive secretary, said the process for selecting a new leader “can’t start soon enough”.

“To be honest, I would be delighted if she announced today she was announcing her resignation and we could then have an orderly election to choose a new leader of the Conservative party,” he told BBC Radio 4’s Today programme.

“I believe the only way we’re going to break this impasse properly is if we have fresh leadership of the Conservative party … If there was an announcement today by the prime minister then of course we could start the process straight away.”

The prime minister, who will chair cabinet on Tuesday morning as talks restart with Labour on the possibility of a Brexit compromise, is also to face a no-confidence motion from Conservative members.

More than 70 local constituency chairs have signed a motion calling for an emergency meeting of the National Conservative Convention, which represents the grassroots membership. This could pass a symbolic vote of no-confidence – though neither the 1922 Committee nor the NCC can force May to step down.

Evans said the combined force of the parliamentary party and the grassroots meant May should “accept the fact the call for her resignation now is growing into a clamour”.

May survived a no-confidence vote last year by 200 votes to 117. It was triggered by enough Conservative MPs writing to the committee to request a challenge.

Many Tory MPs from the centrist wing of the party are keen for the prime minister to stay on for a bit longer in an attempt to avoid a hard Brexiter taking over.

Rory Stewart, the prisons minister, backed May to stay on, saying the problem was not her leadership but deep disagreement in the party on delivering Brexit.

“The idea somehow that some new, fresh leader with extraordinary charm and nimble feet would be able to suddenly get the deal across the line is mistaken,” he told the Today programme. “It’s nothing to do with the individual; it is that people disagree deeply over Brexit.”

There are limited expectations of a breakthrough from the Brexit talks between government ministers and Labour, which are due to resume as parliament returns on Tuesday.

A government team including David Lidington, May’s de facto deputy, and the Brexit secretary, Steve Barclay, is to meet Barclay’s Labour shadow, Keir Starmer, the shadow business secretary, Rebecca Long-Bailey, and others at the Cabinet Office.

Other talks are scheduled, but none are as yet due to include May or Jeremy Corbyn. The Labour leader is scheduled to spend some of the first parliamentary day after the Easter recess meeting the young Swedish climate activist Greta Thunberg.