The London Evening Standard said that Cameron and his family have chosen Larry, a 4-year-old tabby cat from Battersea Dogs and Cats' Home.
A spokesman for Number 10 told PA: "I can confirm that we are getting a cat."
Larry is thought to be moving into his new home later this week. The news follows recent sightings of rats outside Number 10 on live BBC and ITV news broadcasts.
Several cats have served as the unofficial 'Chief Mouser to the Cabinet Office' over the years. Wilberforce, a black and white cat, has the longest tenure, serving four British Prime Ministers between 1973 and 1987.