The 36-year-old man was involved in collision with the cyclist just before 8pm on Friday while Leeds United were playing at Elland Road v Middlesborough.
He suffered a serious head injury and remains in hospital in a serious but stable condition.
The cyclist involved didn’t remain at the scene.
Emergency services attended and the road was closed for a short time.
A West Yorkshire Police spokesman, said: "Officers are now appealing for anyone who witnessed the collision to get in contact with police.
"Anyone with information is asked to contact the safer roads team on 101, or by using the West Yorkshire Police live chat facility, quoting log number 1759 of 31/08."