A 41-year-old man was found seriously injured on Dalsholm Road in Maryhill at around 4.15pm on Saturday, said Police Scotland.
He was taken to hospital for treatment.
Officers believe a burnt-out black Ford Kuga may be linked to the incident. It was found on a cycle track near Kelso Street and Dumbarton Road shortly before 4.30pm on Saturday.
Detective Inspector Craig Warren said the force believes the attack to be targeted and it is being treated as attempted murder.
He said: “I would ask if you were in the area at the time and noticed this vehicle or anyone acting suspicious near Dalsholm or Dumbarton Road, that you come forward and speak to police.
“If there are any motorists with dashcam footage that could assist with our inquiries, please get in touch with officers.”
Police can be called on 101 quoting incident 2595 of Saturday September 11 or anonymously to Crimestoppers on 0800 555 111.