On June 2, Mark Jenkins was riding a Piaggio on Mortimer Road before colliding with a black Land Rover Discovery at 8.15pm.
The 58-year-old was taken to hospital but died from his injuries the following week.
A 47-year-old man from the Stocksbridge area was arrested on suspicion of causing serious injury by dangerous driving, failing to stop and driving while unfit through drink or drugs.
He has since been released under investigation.
A spokesperson for South Yorkshire Police said: “Anyone who witnessed the collision or saw the vehicles before the incident is urged to contact police.
“Officers are particularly keen to speak to the driver of a white Ford Ranger, who may have witnessed the collision.
“We would also like to hear from anyone who has dash cam footage. If you can help, please call 101 quoting incident number 930 of June 2.
“Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website or by calling their UK contact centre on 0800 555 111.”