Carlisle City Council hopes to raise around £4.5m from the sale of land at the Raffles estate to a registered social housing provider.
The council signed a 10-year agreement with Lovell's, the social housing builder, in 2003 to deliver 37 units for rent at an affordable level.
The Homes & Communities Agency said in April it would provide grant funding to enable the development to be completed.
The council is now seeking a registered provider to acquire the land and manage the properties, taking homeless nominations from the council to fill the accommodation.
The deadline for expressions of interest is 3 October.