The 24-year-old was discovered in Wallacewell Road in the Balornock area of Glasgow at about 1am on Saturday.
He is said to be in a stable condition in Glasgow Royal Infirmary with serious head and face injuries.
A man with a dark jacket was seen running away from the scene into a lane next to No 231 Wallacewell Road, police said.
They believe the victim was assaulted and officers are carrying out door-to-door inquiries in the area.
Officers want to trace members of the public shown on CCTV, particularly a man who was walking a dog at around the time.
Detective Constable Peter Chatham said: "At this time, we don't know exactly what happened to the victim.
"We know that members of the public tried to help him and contacted emergency services.
"We are trying to piece together the man's movements and I am appealing to anyone who was in the area at the time and to local residents living in that street to contact us.
"Any small piece of information could prove vital in helping us establish what happened."
Anyone with information is asked to contact Police Scotland on 101 or Crimestoppers on 0800 555 111.