Rishi Sunak looks set to duck out of the vote on the privileges committee report on Monday.
MPs are set to vote on whether to remove Johnson’s access to parliament on his birthday next week.
Penny Mordaunt, leader of the House of Commons, said MPs will debate the privileges committee report before putting the only yet-to-be decided matter (whether he should not receive a Parliament pass) to a vote shortly after.
Johnson was found to have committed “repeated contempts” of Parliament by deliberately misleading MPs with his partygate denials before being complicit in a campaign of abuse and intimidation by the cross-party investigation.
Branding him the first former prime minister to have ever lied to the Commons, the Privileges Committee recommended a 90-day suspension which would have paved the way for a by-election if he had not quit in anticipation.
His resignation means he will escape that punishment but the committee recommended that he should not receive the pass granting access to Parliament which is normally given to former MPs.
It will be a free vote, Sky News understands, meaning MPs will not be told how to vote by party whips.
But Sunak is unlikely to be there.
Jacob Rees-Mogg, a leading ally of Johnson, has predicted that the prime minister will abstain during Monday’s vote on the privileges committee report.
Asked during an interview on LBC how Mr Sunak should vote, Rees-Mogg replied: “Rishi Sunak will abstain on the basis that it is a parliamentary matter”.
Damian Green, the former first secretary of state and de facto deputy PM under Theresa May, said that he is “intending to vote for the committee’s report” and suggested fellow Conservative MPs should not “run away” from the committee’s findings.
Asked if he believed it was important for Mr Sunak to vote for the report, Green told the BBC: “I think personally it is such an important act that deliberately abstaining is not really rising to the importance of the occasion.
“Clearly it is very, very unusual if not unique to have this kind of report on a former prime minister and I am going to vote for it with a heavy heart, with sadness… I don’t want to be doing this but it seems to me the report is very clear cut and parliament should respect its own procedures.”
Related: Guto Harri shredded after suggesting Johnson has been ‘deprived of a livelihood’ by Partygate report