Current rules of the Conservatives’ 1922 Committee mean that the party leader cannot face a second no-confidence vote within 12 months of a first.
Boris Johnson survived a no-confidence vote earlier this month, but the scale of the rebellion shocked many – with the Prime Minister surviving by 211 votes to 148.
The 1922 Committee could change the rules to allow another no confidence vote, and elections to the committee take place on July 21.
One MP, Andrew Bridgen, has said he will stand for the committee on the basis of seeking to change its rules.
Shrewsbury & Atcham MP, Daniel Kawczynski has voiced his ‘strong opposition’ to any potential changes, while Wrekin MP Mark Pritchard and Telford MP Lucy Allan also rejected calls for alterations to the rules.
Montgomeryshire MP, Craig Williams said he would be ‘amazed’ at any change, while Philip Dunne, who was part of the rebellion and warned the issue was not over despite the Prime Minister winning the vote, said he did not want to comment on “an internal party matter”.
Mr Kawczynski said: “I am strongly opposed to any changes in the 1922 constitution with regards to vote of confidence rules for our leader.
“To change them now would be an assault on what we have always cherished which protects us all. Namely complying with the rules and respecting the outcome of a vote.
“The PM has won the confidence of the party. We need to get behind him and work as a team to take on Sir Keir or his successor at a General Election.”
Mr Pritchard said: “The PM just won a vote of no confidence. Under existing rules there can be no new challenge for another year. As a former secretary of the 1922 Committee, I do not support a change in the rules. The PM now needs to be allowed to get on with his job and govern.”
Ms Allan said: "A vote has been held and most colleagues respect the outcome. I would not support changing the rules to try to get a different answer. It is time for MPs to support the Government in dealing with the very difficult challenges the country faces, instead of continuing to focus on internal party issues.”
Montgomeryshire MP, Craig Williams, said: “I think it is incredibly unlikely that the ‘22 would change its rules and if they do, whether is would be retrospective or not.”
He added: “I would be utterly amazed. It is up to Graham Brady and the new committee but I would be very surprised.”
It comes after a weekend where Mr Johnson said he is “thinking actively” about fighting the next two general elections to become the longest-serving post-war leader.
Asked at the G7 summit in Germany on Sunday if his ambitions were delusional, Mr Johnson said: “What I’m saying is this is a Government that is getting on with delivering for the people of this country and we’ve got a huge amount to do.”
He said the “golden rule” is to “focus on what we are doing” – to address the cost of living, the “massive” plan for a stronger economy, and “making sure that the UK continues to offer the kind of leadership around the world that I know our people want”.