The newspaper cited anonymous industry sources who said the company is looking for sites between 3,000 and 5,000 square feet in size for the Amazon Go store.
The Telegraph's report said Amazon's U.S. team was behind the move, which may see the company open a store at Oxford Circus, the junction between London's Oxford Street and Regent Street.
The e-commerce company opened its first Amazon Go store at its Seattle campus in January, where people swipe their Amazon Go smartphone app onto a sensor to enter, pick up groceries, and leave without having to go to a checkout or pay at a register. Amazon says it uses computer vision, algorithms and sensors to detect the items a shopper has picked up, before that person's account is charged. There are now seven Amazon Go stores in the U.S., and the company is considering opening 3,000 stores by 2021.
The U.K. is an important market for Amazon, which said it had seen "record levels" of shopping in the country at the start of its Black Friday sale. It has hired 20,000 seasonal workers for this year's holiday period.
Amazon had not responded to CNBC's request for comment at the time of publication.