Alchemy Developments has applied for planning permission to build the eight houses which are being designed by Arka Architects.
A separate planning application has already been submitted to build seven houses and eight flats on a neighbouring piece of ground.
Redevelopment has been on the cards since 2012, when the club closed for the last time despite a community campaign to retain its facilities, which included a bowling green and tennis courts.
The site has been vacant ever since.