The 24 new homes, off Swinegate, would be one and two-bedroom flats for people on the South Kesteven District Council housing register - those who most urgently need a home.
Cabinet Member for Housing and Planning, Cllr Robert Reid, said: "This development would help SKDC deliver much-needed high quality new social housing to Grantham - something that is needed in our towns, throughout the district and across the country as a whole.
"These properties would be built to the Lifetime Homes standard to support the changing needs of residents now and into the future. They are designed to be inclusive, accessible, adaptable, energy efficient, sustainable and good value.
"This is an exciting proposal and would improve the local area."
The development would form part of SKDC's Housing Strategy and demand shows a requirement for 128 properties to be built in central Grantham. Developing homes in line with demand also helps free up larger properties within SKDC's stock to ensure more residents have a home that suits their needs.
SKDC has already consulted organisations including Lincolnshire County Council Highways and Grantham Civic Society.
The public consultation will be open for responses between Monday 26 October and Sunday 8 November.
The full details and survey can be found by searching for "Swinegate Development" on the SKDC website.
After a planning application is submitted, people will also be able to formally comment on the proposal to the SKDC planning department.
The proposal's strong street line along Swinegate is in keeping with the rest of the street. At the rear, the block is stepped away from neighbouring properties to minimise overlooking. This also allows the buildings to centre around a communal entrance courtyard.
The garage site has existing planning permission for nine flats and SKDC's proposal would expand that to 24 one and two-bedroom apartments.
The 700sqm site is at the northern end of Swinegate, next to Watergate carpark and close to Brook Street.
There are residential properties to the north and east with a mixture of commercial and residential to the south and west, while on the immediate southern boundary is Watergate car park.
Anyone unable to access the survey and information online can obtain all details by contacting the SKDC development team on 01476 406080 or SwinegateDevelopment@Southkesteven.gov.uk