Battersea Cats and Dogs Home has put forward five candidates for the position of Downing Street's resident dog.
The Prime Minister is understood to have raised the prospect of bringing in a pooch to Number 10 earlier this week, which went down well with staff at the address.
Among Battersea's proposed pups suitable for Number 10 is seven-year-old Shih Tzu Barney, who has a "scruffy head of hair", and eleven-month-old mongrel Hank, who "knows how to hold a room".
Also in the mix is a middle-aged Jack Russell Terrier named Puppy, a young Lurcher called Popcorn and "gentle giant" mongrel, Obi.
Mr Johnson declared that he wanted to end the ongoing feud between Downing Street cats Larry and Palmerston, suggesting bringing a dog into the mix.
Larry the cat holds the role of chief mouser in Downing Street
Both cats, as well as Treasury mouser Gladstone, resided at Battersea before living alongside the political elite.
Battersea's head of operations, Rob Young, told talkRADIO: "Battersea has a great relationship with Downing Street when it comes to rehoming animals.
"If we are asked to help Mr Johnson adopt a new companion, our priority will of course be to look for a dog that is comfortable with living in a busy environment, and could happily live alongside chief mouser Larry, who we rehomed to the political corridors of power almost a decade ago."
Chief mouser Larry was originally brought in by David Cameron to deal with the Downing Street mice. It is unclear whether Mr Johnson would give the dog an official role.
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.