A woman in her 80s was hit by a BMW as she walked along a pedestrian crossing on Lozells Road on April 10.
After hitting the woman, the driver failed to stop at the scene.
The woman remains in hospital with injuries to her foot and head.
Police have carried out enquiries around the vehicle, but the person who registered the car is believed to have given a false name and address, meaning we are unable to trace the real owner of the car.
PC Jordan Keen, from the traffic investigation unit, said: “We are urgently appealing for anyone who recognises this man or who was in the area at the time and has dashcam footage or who has not yet come forward.
“This man clearly showed no regard for the elderly woman he knocked down before callously driving away.
“The car has a distinctive white left wing mirror, so someone must recognise the car or know who the driver is.
“We are urging him to do the right thing, and hand himself in."
Anyone who recognises him, or has any information, contact the traffic department on firstname.lastname@example.org, via live chat on West Midlands Police's website or by calling 101, quoting log number 2578 of 10/04/21.
Crimestoppers can be contacted anonymously on 0800 555 111.