The incident happened in Royal Exchange Square at around 3.10am on Sunday.
It saw a 21-year-old man and a 20-year-old woman assaulted by a group of three, all believed to be in their twenties.
The man sustained cuts to his forehead and ear during the assault and the woman was kicked in the stomach.
The four suspects - two men and two women - spoke with “foreign accents” and are believed to have been within Light Nightclub at Royal Exchange Square prior to this incident taking place.
Both the male suspects are described as white and approximately 5ft 10in tall.
One had dark curly hair and was wearing a printed t-shirt.
The other had dark hair tied up in a bun and was wearing a white t-shirt.
One of the female suspects is described as being around 6ft with dark hair and wearing a leopard print top.
The second had short dark hair worn in a middle parting.
Detective Constable Leigh-Anne Sutherland at Glasgow City Centre CID said: “The city centre would have been busy at the time of the incident with people leaving night clubs and therefore we are appealing for any passers-by who were in the vicinity around that time and may have either witnessed the incident or seen the four suspects in the area to contact us.
“There is a number of CCTV cameras in the area and we are currently reviewing footage to gain further information.
“Anyone with any information should contact police at Glasgow City Centre Police Office via telephone number 101 quoting incident number 0789 of 12 May 2019.”