This week, 72 MPs signed a pledge to oppose the “divisive and discriminatory” scheme.
Critics of a vaccine certificate have branded the idea oppressive.
Government adviser Professor Robert West also warned that a Covid passport would give people a false sense of security.
A Whitehall source told the Daily Mail that ministers would try to win round rebel Tory MPs by reassuring them that the scheme would be temporary.
The source said: “It will be time-limited and I think the duration of the scheme will be measured in months.
“The party will not wear any longer.”
Mr Johnson is expected to give a major announcement on Monday to address vaccine passports, the Government’s plans for holidays and the next phase of lockdown.
“But it may be a way of ensuring we can get more people back doing the things they love.”
Tory MP Andrew Bridgen said the backbench opposition to Covid certificates was to do with principal rather than about the duration it will be in place.
He described the idea of a vaccine passport as a “vision of hell”.
According to the Daily Mail, Mr Bridgen said: “Who would have thought the British public would ever have to show their papers to go to the pub?
“The whole idea is like something out of North Korea, and I hope that the strength of feeling, not just on the Conservative benches but across Parliament will stop the Government heading off in this direction.”