The Belgian defender appeared to be subjected to abuse by a supporter during a television interview following Monday's victory over Manchester United at Old Trafford.
Abusive comments were allegedly heard during the Belgian's post-match interview alongside James Milner for Sky Sports in the aftermath of City's 2-1 victory at Old Trafford.
The footage in question has now been handed to the police despite neither Kompany nor his club lodging an official complaint regarding the matter.
A police statement read: "Greater Manchester police have not received a complaint about racist abuse directed towards any players following last night's fixture, however we have now been made aware of this footage by the Manchester Evening News. "The force will work with both clubs and review any footage to investigate the incident."
The incident marks the second Manchester derby controversy this season, after United defender Rio Ferdinand was struck by a coin following Robin van Persie's late winner at the Etihad Stadium in December.