Police found the 21-year-old man with a serious leg injury after officers were called an address in Stainbeck Road at Meanwood just after 4.30pm on Monday (Nov 19).
He was taken to hospital for treatment and his injuries were confirmed as being consistent with a single gunshot wound.
His injuries are not life threatening and he is continuing to receive treatment.
Police had received a report of a road traffic collision at 4.35pm at the junction of Stainbeck Road and Potternewton Lane.
It is believed the collision is linked to the shooting.
A grey BMW 320 M Sport, registration YK18 SSC, was involved in a collision with a black Nissan Micra.
The occupants of the BMW, described as two black males, ran off from the scene – one in the direction of the Beckhill estate and the other towards Meanwood.
The driver of the Micra, a 33-year-old woman, was not seriously injured but was left badly shaken
She was taken to hospital for treatment.
Detective Inspector Andy Cass, of West Yorkshire Police Homicide and Major Enquiry Team, said: “We are still speaking to the victim of the shooting to get a clearer picture of what happened but we have not yet been able to confirm where the incident took place.
“We believe the collision involving the BMW is linked to the shooting and we would like to hear from anyone who has seen that vehicle in the area at any point in the time leading up the crash, particularly if they witnessed anything that may have the shooting itself.
“We would also like to hear from anyone who saw the men running off from the scene of the crash or who has any information that could assist the investigation.
“The criminal use of firearms on our streets is completely unacceptable and is always something that we will treat very seriously.
“We are actively carrying out enquiries to identify those responsible and have specialist detectives working alongside armed officers to progress the investigation.”
Anyone with any information that could assist the investigation is asked to contact the Homicide and Major Enquiry Team via 101 quoting Operation Plantdeat or call the independent charity Crimestoppers anonymously on 0800 555 111.