Some Tory MPs are also looking at Mr Johnson as a potential party leader.
Mr Johnson’s public profile has been enhanced by the London Olympics, and on Monday he upstaged Mr Cameron with a crowd-pleasing speech at a parade of Olympic athletes.
Mr Johnson has also openly criticised Mr Cameron recently over a potential U-turn on Heathrow airport expansion.
He has, however, flatly denied accusations of manoeuvring to win the leadership.
A “radical” new Conservative group was forced to deny it was not trying to undermine Mr Cameron or promote Mr Johnson’s leadership prospects, one of its founders has said.
Conservative Voice was founded yesterday with the backing of senior Tory Right-wingers including David Davis and Dr Liam Fox.
The creation of the group, which wants more focus on issues such as tax cuts, Europe and social mobility, coincides with whispering among Conservative backbenchers about the Prime Minister’s leadership.
Both Mr Davis and Dr Fox are also previous Conservative leadership candidates, defeated by Mr Cameron in 2005.
But Don Porter, the founder of Conservative Voice, insisted that the group was not a threat to Mr Cameron’s authority or a vehicle for leadership challengers.
Mr Johnson, a Daily Telegraph columnist, would need to become an MP again before he becomes leader.