The lone, male cyclist was travelling along the cycle track between Beaumont and St. Aubin on Saturday.
The police are seeking to track down a runner who may have seen the incident and was jogging from St. Aubin towards Beaumont at around 06:00.
The runner has been described as having a tanned complexion, dark hair and being of slim build and is known to have spoken to two other members of the public in the area of the incident.
Anyone else who may have seen the cyclist, or has CCTV or dashcam or who has any information is asked to call the police on 612612 or to contact independent charity Crimestoppers anonymously on 0800 555111 or via their anonymous online form.