Spenhill, a Tesco subsidiary, held a public exhibition showing designs for a new store last weekend.
Plans for a new store in The Broadway, also include 65 new homes, a cafe and a library.
Spenhill and Tesco currently own the site of Stanmore library, in Stanmore Hill, which they lease to Harrow Council.
It would also need to acquire the site of a former multi-storey car park next to Lidl, behind The Broadway, from the Council in order to progress its plans. Stanmore library would be demolished, along with Anmer lodge, a homeless shelter.Tesco says it would re-house residents of Anmer Lodge.
The planned store, would be 20,000 sq ft, with a 400-space car park. Tesco and Spenhill will now have to apply for planning permission from Harrow Council. Councillor Marilyn Ashton was at pains to point out, "there is no partnership, agreement or commercial arrangement between Tesco and the Harrow Council".