Crews were alerted to the fire on Balornock Road in the Springburn area of the city at around 6.20pm on Sunday evening.
Local residents spotted a thick plume of black smoke billowing above the disused hospital’s clock tower.
The Scottish Fire and Rescue Service confirmed they were in attendance.
And a spokesperson for Police Scotland said: “Police were called at 6.19pm this evening to assist the fire service.
“We may assist with road closures however the main roads are still open.”
More to follow.