Reports on social media show crews on Carlton Place in the Gorbals area of the city.
The building faces the River Clyde and sits close to Glasgow Sheriff Court.
Reports suggest crews arrived at the scene at 8pm tonight.
The BBC report the former Prince and Princess of Wales hospice building is on fire.
The historic B-Listed property has been unoccupied since 2018, when a new £21m hospice opened in Glasgow’s Bellahouston Park.
MSP Paul Sweeney said: “Another fire at the historic Carlton Place terrace.
“This one is more severe and has taken hold in a section of the roof.
“Thankfully, the firefighters have contained the fire in the attic space and are bringing it under control.
“We need urgent council intervention to save it now.”
Images on X show the roof on fire with flames ripping through the structure.
It is understood that there are both residential and business properties in the area around Carlton Place.
Social media users took to X to share images of the fire.
