But it's not one of the retail giant's fierce rivals - it's Thomas Green's, the franchise business that focuses on opening stores selling British products to appeal to ex-pats and adventurous locals.
Thomas Green's is in the midst of an expansion drive in Continental Europe, where it has 10 franchisees in Spain, France and the Netherlands. This number is expected to double this year, with plans for a network of 50 stores within three years.
Once these stores are up and running smoothly - expected to be in five years - the company will focus on big cities in the US, said MD Philip Evans. "We consistently get emails from people in the States asking if we can set something up there.
"Admittedly, getting stuff into the US is difficult. But it's part of our long-term plans. There are hundreds of little shops in the US so we're not going to set ourselves up in remote outposts. But big cities on the east and west coasts of the States are viable."
However, Thomas Green's transatlantic offer would not be in direct competition with Tesco, he insisted. "Tesco will be taking British retail skills to the US to sell US products.
"We'll be taking British retail skills and British products."
Thomas Green's stores are supplied by Nisa International.