The 22-year-old was found in Muirhead Drive, close to its junction with Knutsford Grove, in the Holme Wood area of the city at about 10pm on Monday.
He had suffered serious head and leg injuries and today, as police issued an appeal for information, his condition was said to be “critical”.
A spokesman for West Yorkshire Police said it was thought a vehicle may have been involved in the incident.
A 31-year-old man has been arrested on suspicion of causing serious injury by dangerous driving and released under investigation.
Anyone with information is asked to ring West Yorkshire Police’s western area roads policing unit on 101, quoting log reference 2264 of November 5.