The defender is thought to have been the subject of jibes of a racial nature while speaking on camera to Sky Sports presenter Geoff Shreeves following City's 2-1 victory over Manchester United on Monday.
It is believed that taunts were shouted at the defender from people behind the camera while he was being filmed.
While the authorities were not informed by either club of any incidents, footage handed to them by the Manchester Evening News has made them look into an alleged case of racism.
"The force will work with both clubs and review any footage to investigate the incident," the newspaper quotes a police statement as saying.
Meanwhile, UEFA have announced they they will impose "harsh" sanctions on European clubs guilty of racism.