Sainsbury's is proposing to open a convenience store at the corner of Long Lane and Weston Street.
The new store, which is the subject of a licensing application to Southwark Council, will occupy the ground floor of a new seven-storey block to be constructed on the site of the former Valentine pub.
Plans for a scheme designed by Hampson Williams incorporating 19 flats were approved by Southwark Council at the end of last year. An earlier proposal by Fereday Pollard received community council approval a year ago.
The new store will be just 430 metres from the Sainsbury's Local store at Bermondsey Square and less than 600 metres from the Borough High Street branch. A fourth Sainsbury's Local store is due to open 500 metres away at Guy's Hospital.