The 31-year-old motorist was rushed to the Western Infirmary after a group of youths stabbed him and vandalised his car at around 2.05am on Sunday.
Police said he was driving his black Vauxhall Corsa along Spiershall Terrace, in Yoker, when the incident took place.
A member of the public dialled 999 after the man was found bleeding in the road.
Detectives were examining CCTV images and appealing for witnesses following the incident, and were unsure why the man, who is not local to the area, was in Yoker or why he was targeted.
Detectives are also still hunting for two sex attackers following the rape of a woman in Govanhill.
Two weeks after a 24-year-old woman was attacked in Dixon Road, officers returned to the scene where they spoke to passers-by who may have been in the area at the time of the incident.
Between 12.30am and 2am on Sunday, plain clothes officers stopped dozens of motorists and pedestrians in Dixon Road and surrounding streets in a bid to gather more information.
They also handed out leaflets to locals.
Previously, police released CCTV images of two men they hope to speak to in connection with the rape, which happened on Monday May 19.
Both had a sallow complexion and dark hair, and were seen in Allison Street near Cathcart Road between midnight and 1.30am.
One of the men was wearing a dark jumper, trousers and white trainers, while the other was also wearing dark clothing.
Footage of the pair has been released on YouTube in a bid to encourage the men to come forward.