The school would be built on the old Adelphi Terrace Secondary School land.
Glasgow City Council is planning to open a school for children living in Laurieston, the Gorbals and the city centre to ease pressure on current schools as the number of homes in the area increases.
The preferred option would see the council develop the site of the former Adelphi Terrace Secondary School.
Glasgow councillors have now agreed to progress to consultation, which will include public meetings, from November 1.
Cllr Chris Cunningham, city convener for education, skills and early years, said: “There are two key drivers for these proposals, the first is the growth of new housing and population in the Gorbals/Laurieston area, with a consequent increase in pressure on the local schools.
“The second is the current and projected growth in the residential population in the city centre, currently sitting at around 20,000 but projected to reach 40,000 by 2035.
“We require to provide additional capacity for the children who will form part of this expanded city centre community.”
Up to 900 new homes are being built in Laurieston and a council report stated the redevelopment has “put pressure on the social infrastructure”.
Council officers’ preferred option is to re-purpose the Adelphi Centre, at 12 Commercial Road. The other option considered involved using an old school building at 5 Florence Street, which is not currently owned by the council.
The Commercial Road option would see an existing two-storey building, owned by the council, refurbished, providing 14 teaching spaces, a dining hall, drama room and music/dance rehearsal space.
There would also be a media library, sensory room and kitchen, but there is not space for a games hall. Officers have suggested the school could use the council-owned Gorbals Leisure Centre, which has a swimming pool, health and fitness suite, games hall and tennis courts.
There would be a playground at the new school, with plans to use an existing car park.
Bailie Soryia Siddique, a Labour councillor for Southside Central, said: “Consultation for the creation of a new primary school on the southside is a positive development.
“Welcomed new housing in Laurieston is likely to increase the need for schooling spaces. There is also an opportunity to include a climate science/STEM education lab space within the school.
“This could be an opportunity for Glasgow to lead the way in climate science education. I look forward to the consultation outcome.”
Public meetings, as part of the consultation process, will be held at Blackfriars Primary at 7pm on November 9 and at Bellahouston Academy on November 17 at 7pm. The consultation period will run until January 5.
The new school would be added to the catchment area for Bellahouston Academy.