It happened at about 11.55am, when a grey Hyundai i10 was in collision with the cyclist by the mini roundabout in Greenfold Lane.
The cyclist, a man in his sixties, suffered a head injury and was taken to hospital, where he is said to be in a critical condition.
The driver stopped at the scene.
Anyone who witnessed or who may have footage of the collision, or who saw the movements of either vehicle immediately prior to it, is asked to contact Roads Policing either by calling 101 or using the options on the West Yorkshire Police website.
The log reference is 0715 of 31 March.