The man was driving a Ford Fiesta on Aldridge Road, Streetly when he was hit by a driver who had allegedly failed to stop for officers prior to the crash.
The driver of the Jaguar XF, a 51-year-old man, is currently in hospital - he will be interviewed by police at a later date.
The force has also referred itself to the Independent Office for Police Conduct in connection with the incident.
A spokesperson for West Midlands Police said: "A 20-year-old man who was in a collision on Aldridge Road, Streetly on October 7 has sadly died.
"The Ford Fiesta he was driving was hit by a Jaguar XF, which failed to stop for police prior to this.
"The driver of the Jaguar XF, a 51-year-old man, remains in hospital and will be interviewed in due course.
"The incident has been referred to the Independent Office of Police Conduct (IOPC) as is normal procedure.
"Our thoughts remain with the man’s family and friends at this incredibly sad time and we have specialist family liaison officers supporting them."
Members of the public who witnessed the crash are being urged to step forward.
Officers are also keen to hear from anyone who may have dashcam footage of the incident.
Anyone who saw what happened or has dash cam footage, and has not already spoken to police, is asked to use live chat on the police website or call 101 quoting log 4525 of October 7.