Cordons remain in place on Servia Hill in the Woodhouse area of the city after officers were called to reports of a confrontation between two groups of males shortly after 5pm on Wednesday, May 9.
Witnesses reported seeing what was believed to be a firearm and hearing loud bangs. Both groups of males left the scene, some in a dark coloured Fiat hatchback.
No evidence of a firearms discharge has been recovered from the scene.
Detective Inspector Dave McDougal, of Leeds District CID, said: “We would like to hear from anyone who witnessed the incident, saw the dark blue Fiat in the area, or who has any information that could assist the investigation."
Meanwhile, the confirmed shooting of a 23-year-old man that took place Burmantofts Street on the same evening is still being investigated.
The victim was later arrested on suspicion of possession of a firearm with intent to cause fear of violence and is currently in custody, but has since been released without charge.
The incident, which took place at around 6.30pm on Wednesday evening, resulted in the male being shot in the shoulder after a silver Mazda 3 forced its way through the traffic and pulled alongside the BMW.
Three black men wearing balaclavas got out of the Mazda.
Two were armed with machetes or bats and began attacking the vehicle before one of the three produced what was believed to be a handgun and fired at the victim, who was sat in the front passenger seat.
The men left the scene in the Mazda, reversing into a car behind it, causing damage, before making off down St Mary’s Street.
The two incidents are not being treated as related to one another.