Reports are building of strained relations between Mr Johnson and Chancellor Rishi Sunak.
A “senior Downing Street source” told the BBC “there is a lot of concern inside the building about the PM” and “it’s just not working”.
Allies of Mr Sunak denied the Treasury was involved in the briefing.
The anonymous source of the incendiary briefing to the BBC has been dubbed the “Chatty Pig” in Westminster, as the comments emerged following the Prime Minister’s CBI speech.
Mr Raab told BBC Breakfast: “It’s the job of Westminster commentators to pick up on one anonymous source from wherever they found it to criticise the Government of the day, that’s fine.”