The plans, which are being considered by Brighton and Hove City Council, give confirmation of the chain’s intention to open on the site which it first announced last year.
The proposals also include a second retail unit, for an as yet unnamed tenant, as well as a 22-space car park.
Vehicles would enter from Preston Road and exit into Cumberland Road .
The branch would be the third Sainsbury’s convenience store to open in the city this year, after the recent opening in Western Road, Hove, and forthcoming store in Portland Road, Hove.
The chain also doubled the size of its Western Road, Brighton, shop last year.
The latest plans have been submitted within a week of the council refusing retrospective planning permission for changes made by Sainsbury’s to the building in Western Road, Hove.
Council leader Mary Mears blogged about her concerns with supermarkets in response.
The council is expected to decide on the Preston Road plans by April 27. To view the application click here.