Two men found the victim lying on Hope Street, near to Argyle Street, at about 04:30 on Friday 19 February.
The man was treated in hospital for a head injury and released. He was re-admitted at a later date and told he needed surgery for a fractured skull.
The incident was reported to police on 3 March. They want to trace the two men who found the man and other witnesses.
Det Con Stephen Palmer said: "A man has been left with a very serious head injury as a result of this attack and inquiries are at an early stage to establish what happened.
"I would like to speak to anyone with information about this incident, particularly the two people who called an ambulance for the victim."
A man found lying in the street in Glasgow had suffered a fractured skull after being attacked, police have said.