The developer has submitted plans to the city council to build 36 affordable homes on a former bowling green off Eccles Old Road in Pendleton.
The development would comprise 22 one-bedroom flats and 14 two-bedroom flats delivered across three blocks.
Salford-based Penbow, whose directors are listed as Hassen Lakhel and Graham Walsh, is in talks with a housing association to help fund the development and take ownership of the apartments once complete.
Subject to planning approval, the developer will submit an application to Homes England for grant funding.
Under the proposals, a two-bedroom detached property on the one-acre site would be demolished to make way for the apartments.
The architect for the project is Pentland Design & Management.