Northern Ireland Secretary Julian Smith is reported to be facing removal from Cabinet after falling out with Number Ten before the general election.
In September, Mr Smith felt it necessary to dismiss speculation after he appeared to contradict a Government official.
As reported by Irish News at the time, a briefing to Spectator magazine suggested Britain might punish EU member states who supported an Article 50 extension.
The article blamed Taoiseach Leo Varadkar and said defence and security co-operation could be affected, Mr Smith tweeted to say this would not have been in the interest of Northern Ireland or the Union.
Work and Pensions Secretary Therese Coffey is also believed to be an insecure position and Defence Secretary Ben Wallace, despite being a close friend of Mr Johnson, may be moved to a different position according to speculation.
Chancellor of the Duchy of Lancaster Michael Gove is thought be near the top of the promotion list.
Mr Gove could be given overall charge of global trade talks.
He is expected to take on responsibility for post Brexit trade talks with the EU.
Chief Secretary to the Treasury Rishi Sunak has impressed Downing Street during Budget preparations and in pre-election debates.
Speculation has mounted a possible move to create a super-ministry containing business and trade portfolios.
Security Minister Brandon Lewis also impressed and could see himself promoted.
There is also a suggestion that Mr Johnson’s adviser Dominic Cummings is behind plans to move control of prisons, probation and sentencing from the Ministry of Justice to the Home Office. Read more
According to the Mail on Sunday, two names facing the sack are Attorney General Geoffrey Cox and Business Secretary Andrea Leadsom. Mr Cox has been accused by sources of not being enough of a team player.