The Pure Gym chain has submitted a planning application for premises in the Shawlands Arcade.
But locals, including MSP Nicola Sturgeon and councillors are opposed to the bid, saying the arcade site should be reserved for shops and cafes.
So far there have been 128 letters of support.
Joanne Grant, who lives nearby, said people were furious about the proposals and want them scrapped.
She said: "There have been 941 objections, yet we are still not confident that this will be refused. No one is listening.
"There are already gyms in the area, there is not enough parking to accommodate this and Shawlands Arcade should be about local businesses for local people."
Nearby residents say the gym will attract noise and anti-social behaviour, while being against plans to revamp the Shawlands area with local businesses.
Resident Kenneth Grearson said: "I get the feeling, and many of my neighbours get the feeling, that no one is listening to us.
"It feels very much like they are going over our heads.
"There are fans on the roof of the building that used to come on at night when cleaners were in the building.
"We had to have that stopped as the noise was dreadful, but if a 24-hour gym moves in then we will have the same problem again."
Proposals, for the Pure Gym, and eight parking spaces, will go before the council's planning committee tomorrow.
Euan MacNeilage is a member of Shawlands Community Council, which is also against the proposal.
He said: "There is already one local gym. This one will take up so much retail space and take Shawlands away from the town centre feel that we are trying to generate.
"We had a meeting with Pure Gym and representatives from the council but they couldn't respond to any of our questions or understand any of our concerns"
A Glasgow City Council spokesman said: "This application will be considered at the planning committee."
A spokesman for Pure Gym said: "Our policy is to ensure that there is always at least one member of staff on-site.
"We also have extensive CCTV throughout our gyms and at all entrances, which are monitored continually.
"We also have alarms linked to the emergency services.
"We have no reason to believe that the gym will cause anti-social behaviour or noise."