Merseyside Police have confirmed they are working closely with both Liverpool and Manchester City after a number of reported incidents at the match at Anfield on Sunday.
Police have been made aware of "offensive and disorderly behaviour" during Liverpool's win over City, including allegations of coin-throwing and offensive graffiti that was sprayed in the away section.
Allegations have also been made that the City team coach was damaged on the back from the stadium after the match had taken place.