In the collision at around 3.10pm on Friday (July 8), a 65 year-old local male cyclist collided with a stationary Mercedes parked on Ludborough Road.
The cyclist was airlifted to Queens Medical Centre with serious injuries.
Police are particularly keen to trace a female who was driving a small blue car, and who may be an important witness.
Any other witnesses are also asked to come forward.
Anyone with information is asked to call 101, quoting incident number 239 of July 8.