The Pure Gym chain wants to open premises in the Shawlands Arcade, but almost 1000 people, including Deputy First Minister Nicola Sturgeon, have objected to the plan.
They say the site in the arcade for the planned gym should be reserved for shops and cafes.
But the city council's planning committee was told moves to market the site for retail have failed, and the arcade owners have warned a section of the development may have to close unless an alternative use can be found.
Part of the problem is that the units at the rear of the arcade have no street presence and as a result suffer from lack of footfall.
A report to councillors says: "The retail units within the arcade as a whole suffer from either prolonged vacancy or short term occupation with high turnover.
"It is evident that the continued marketing of these units in their current form is no longer viable and appropriate alternative uses must be considered.
"It is accepted that due to lack of demand in retailing in this location, other uses must be considered as failure to do so may result in the closure of this area of the arcade which would be of greater detriment to the future of the Shawlands Town Centre and the surrounding area than the provision of alternative non-retail uses."
Councillors were told if a gym was to open it would result in around 30 new jobs for management, personal trainers and cleaners.
Some objectors have raised concerns the gym will cause anti-social behaviour and noise.
But councillors were told: "It is not considered gym use would result in any additional anti-social behaviour issues, specifically in consideration to the consumption of alcohol, as there are no licensed premises included within this development."
A spokesman for Pure Gym said: "We have no reason to believe the gym will cause anti-social behaviour or noise."
Councillor decided to hold a hearing in the next couple of weeks to hear views from both sides before making a decision.