The business secretary is understood to have fallen out with Mr Gove after he had an affair with one of her friends.
The levelling-up secretary, who is divorced from columnist Sarah Vine, went on to have a relationship with the female friend of the business secretary, according to The Times. The woman has since separated from her husband.
In an interview with The Times this week, Mr Badenoch confirmed the story for the first time. “He did something that was very, very annoying,” she admitted.
When asked by Trevor Phillips what the “very annoying” thing was on Sunday (11 February), Mr Gove replied: “Me being me, there are plenty of things I do that irritate my colleagues from time to time.”