Developer Gleniffer Estates has lodged a planning application with East Renfrewshire Council to develop a third phase at its Greenlaw Village site in Newton Mearns.
The nine-acre site has already attracted Scotland's first new-build Waitrose store and other big high street names, including a Tesco Express and Premier Inn/Beefeater.
If the latest planning application is successful phase three will offer three more retail units, spanning 6000 sq ft, 7000 sq ft and 6924 sq ft respectively.
No details of cost have been revealed but, if approved, the developer hopes units will be available for occupancy next spring.
Bryan Wilson, managing director of Gleniffer Estates, said: "Since its launch three years ago, Greenlaw Village has attracted a tremendous number of visitors each week and most occupiers have reported greater than expected sales.
"The first two phases were sold at prices exceeding expectations. We are confident that if planning is successful then phase three can further enhance the facilities available and bring further new jobs to the area.
"We have received strong interest in the scheme and are in discussions with a number of first class retailers."
No date has yet been set for the application to be considered.
But plans for the site include a further two development phases, which already has a retail parade featuring high street brands, including Vets 4 Pets, Barnardo's, and BetFred, as well as a number of local retailers.
It also includes a contemporary Indian restaurant, called Zyka, on a 4000 sq ft standalone site, which was sold to the owners.
The restaurant, run by husband and wife team Indy and Billie Lalli, won plaudits for offering two different cuisines – European and Indian – produced by two separate kitchen teams in one location.