The Prime Minister is understood to have raised the prospect of bringing in man's best friend when he addressed staff in Number 10 for the first time.
Mr Johnson began by declaring that he wanted to end the feud between Downing Street cat Larry, and his rival across the street at the Foreign Office, Palmerston, who famously do not get on.
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He then apparently suggested the idea of getting a dog - to cries of approval from the assembled staffers.
Insiders acknowledged that any new four-legged resident of Number 10 would have to get on with Larry, who was originally brought in by David Cameron to deal with the Downing Street mice.
"It would have to be a dog and a cat that get along," one source said.
It is thought that if Mr Johnson does go ahead with the idea, he is most likely to go for a rescue animal, possibly, like Larry, from Battersea Dogs and Cats Home.
However a decision may be some way off.
"It is a longer-term project," the source said.
The last resident of Downing Street to have a pet dog was George Osborne, who brought in a Bichon Frise called Lola when he was chancellor.
Her arrival was reported to have led to the family's cat, Freya, being exiled to the Kent countryside, amid claims that she had been "bullying" her diminutive housemate.