Police were called to Dundasvale Court, Cowcaddens after the body was found just before midnight on Saturday.
Officers investigating the incident say that one line of enquiry is that the man fell from a nearby flat.
Officers are trying to piece together the final movements of a man found dead outside a block of flats in Glasgows city centre.
Police were called to reports of a mans body being found at Dundasvale Court, Cowcaddens, around 11.50pm on Saturday.
It is not know how the man died but officers are looking at whether he could have fallen from one of the flat windows.
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Locals reported seeing the body outside the block of flats and a large police presence on Sunday morning.