The current site is "pretty terrible", a councillor says.
A seven-storey holiday apartment block is being built on Blackpool seafront.
The owner of Premier Inn wants to flatten the site to add more rooms and student flats.
It follows a woman being sexually assaulted in her room by a man in Maidenhead, Berkshire.
The Sauchiehall Street site is known to many city residents as the C & A building, and was also the home of Dunnes Stores.
Charles Dickens, King George II, Admiral Lord Nelson and The Beatles have been through its doors.
The new generation of hotel spas is selling treatments that promise better sleep, lower stress and longer, healthier lives.
Robert Gordon's College is calling for the issue to be addressed after plans were submitted for a nearby site.
Jason McKelvie says Stirrups Hotel could see its annual rates rise by almost £150k over the next three years.
