Officers said the crash, which involved a silver Volkswagen Golf driven by a 79-year-old man, took place between 09:40 and 09:50am on Monday near the Iceland store on La Rue à Don.
The cyclist died later that morning as a result of the collision.
Police have said they are particularly interested in hearing from anyone who may have seen what happened, as well as any drivers who were driving in the area at that time or those who may have dash-cam footage relevant to the investigation.
Anyone with any information can contact the police on 612612 or the independent charity Crimestoppers anonymously on 0800 555 111 or via their anonymous online form.