The man - who has yet to be identified - was knocked down on Scotland Road in the Vauxhall area of the city near the Wallasey Tunnel at around 6.50pm.
The victim is understood to have been pronounced dead in hospital.
The incident has been reported to the Independent Office for Police Conduct (IOPC), which has launched an investigation.
An IOPC spokesman said: "Merseyside Police has referred to us a fatal collision involving a police car and a pedestrian on Scotland Road in Liverpool this evening.
"We have sent investigators to the scene.
"Following a brief assessment, we have decided to carry out an independent investigation."
Merseyside Police have been contacted for comment.
A witness told the Liverpool Echo that he saw the police car hit the pedestrian as he was crossing the road.
He said: "Two police officers were trying to hold the man. I offered them a bottle of water in case they needed it but I didn't want to get in their way."
Other witnesses told the Echo that the police car had its blue lights flashing at the time of the collision.