The Sauchiehall Street branch of the sandwich shop chain was covered in police tape on Tuesday morning.
Piles of burnt rubbish could be seen strewn across the ground on the West Nile Street side of the building.
Shattered glass was lying in a pile along the bottom of one of the windows which had been smashed.
Police Scotland has been contacted for comment.
We will bring you more on this as we have it.
