The driver was behind the wheel of a silver Lexus LS2000, which failed to stop for officers in the Holywell Road area of Wincobank.
Two police cars were involved in a pursuit of the vehicle, which then crashed into a telegraph pole opposite Rothay Road.
The Lexus hit a parked car and the driver fled.
A South Yorkshire Police spokesman said: “at around 6.15pm on Thursday, January 7, it is reported that a silver Lexus LS200 car failed to stop for officers in the Holywell Road area of Sheffield.
“Two marked police cars pursued the Lexus when, opposite Rothay Road, it was reportedly involved in a collision with a telegraph pole.
“The pole broke and fell onto a parked car, causing minor damage.
“The driver of the Lexus is alleged to have fled the scene after getting out of the car.
“Nobody is believed to have been injured during the incident and officers are keen to speak to witnesses or anyone with information about the driver.”
Anyone with information should call South Yorkshire Police on 101, quoting incident 850 of January 7, or Crimestoppers on 0800 555 111.