The Newton Mearns branch of New Look is among a list of 60 which could close across the UK.
The fashion company has announced plans to axe up to 980 jobs claiming it has struggled with an “extremely challenging” retail environment.
Alistair McGeorge, executive chairman of New Look, said: “Given our challenged trading performance and over-rented UK store estate, we are having to take tough but necessary actions to reduce our fixed cost base and restore long-term profitability.
“We have held constructive discussions with our key landlords and strategic partners and will now seek creditor approval on our CVA proposal.
“A priority for us is to keep all potentially affected colleagues informed during this difficult time.”
A decision will be made on New Look’s CVA on Wednesday, March 21.