Port of Leith Housing Association has submitted plans to the Council to build 11 flats on the site of the shop in Telford Drive.
The project will see the shop being demolished and replaced it with a residential block containing 11 units over four storeys.
They will build one and two-bedroom flats, along with associated external works, recycling and refuse store and landscaping.
The architect stated: “This car free development will provide affordable housing for a wide range of residents, creating a modern and attractive place to live.
“The site takes advantage of the neighbouring green spaces and views over the adjacent and popular walking and cycle route, Telford Path.”