The school would be built on the old Adelphi Terrace Secondary School land.
The proposal, for land previously used by the former Adelphi Terrace Secondary School, is set to go out to public consultation from November 1.
It is being recommended to ease the pressure on existing schools in the Gorbals and Govanhill as more homes are built in the south of the city.
Cllr Chris Cunningham, city convener for education, skills and early years, said: “As part of Glasgow’s ambitions to regenerate the Gorbals/Tradeston/Laurieston and Govanhill areas of the city, a significant amount of new housing has been constructed in these neighbourhoods.
“As a result of this, a number of schools have experienced increasing rolls, and steps have had to be taken to ensure that there was sufficient capacity for catchment area children.”
Under plans to transform Laurieston, up to 900 new homes are being built on 13 hectares of land. The redevelopment has “put pressure on the social infrastructure, and in particular, the schools serving the local area”, a report by Cllr Cunnningham states.
Two options have been proposed by council officers, with option two, repurposing the Adelphi Centre, at 12 Commercial Road, preferred. It was formerly the Adelphi Terrace Secondary School.
The other option involved using an old school building at 5 Florence Street, which is not currently owned by the council.
If the preferred option is taken, the existing two-storey building, owned by the council, would be refurbished into 14 teaching spaces, a dining hall, drama room and music/dance rehearsal space.
It would also include a media library, sensory room and kitchen. There isn’t space for a games hall, but “an alternate arrangement to consider would be for the school to use the council-owned Gorbals Leisure Centre”.
The leisure centre, which would be a short walk from the school, has a swimming pool, health and fitness suite, games hall, tennis courts and a dance studio.
A playground could be created on the existing car park and the council reports an internal transfer of the site “would be straightforward should the proposal be agreed”.
Public meetings on the proposal will be held at Blackfriars Primary at 7pm on November 9 and Bellahouston Academy on November 17 at 7pm. The consultation period will run until January 5, 2022.
The primary school would be associated with Bellahouston Academy, and would be added to the catchment area.