And they are keen to trace a Good Samaritan who helped the victim as he lay injured on the ground.
The 22-year-old was walking through Govan at 12.30am on Saturday when he was approached by a group of men who chased him.
He stumbled and fell then was attacked, sustaining serious back injuries.
The group of men ran off, leaving the victim lying on the ground where he was helped by a local resident.
Shortly afterwards, the victim's two friends drove past in a black Ford vehicle and took him to the Glasgow Royal Infirmary.
The victim is currently still in hospital, where medical staff described his condition as stable.
There are no descriptions of the men involved in the attack on Brand Street, which police said was not random.
Detective Sergeant Jane Lawson said: "This was a very frightening experience for the young man concerned, although we do not believe it was a random attack.
"I'd like to speak to anyone who was in the vicinity of Brand Street at the time of the incident and who may have information which may assist us with our inquiries.
"We know that a householder from nearby assisted the victim shortly after the attack, and as yet we have been unable to trace the Good Samaritan.
"I'd like them to get in touch as soon as possible."
Anyone with information is asked to contact Govan CID on 101.