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.
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On that alleged incident, Merseyside Police said: "We have also been made aware of an allegation that a Manchester City team coach was damaged. However no incidents have been reported to us or that items were thrown at the coaches, and we are now working with MCFC to establish the circumstances of what happened and the allegation that damage was caused."
A statement from the force on all the allegations added: "Such behaviour will not be tolerated, and we are working with both clubs to identify and bring to justice anyone found responsible for committing offensive and disorderly behaviour.
"Anyone with information is asked to contact Merseyside Police social media desk via Twitter @MerPolCC or Facebook ‘Merseyside Police Contact Centre’ quoting reference 289 of 16 October. You can also call 101 or contact the independent charity Crimestoppers anonymously on 0800 555 111."
Liverpool won Sunday's encounter 1-0 after a second-half goal from Mohamed Salah.
According to a report from the Manchester Evening News, the windscreen of City's bus was cracked by an object en route back towards the M62 from Anfield Road. City have not released a statement about the alleged incident, but Liverpool said on Sunday night that an investigation would be underway to identify anyone who threw coins at Guardiola during the game.
Last night, Liverpool also condemned what they labelled as "vile chants" around Hillsborough and Heysel coming from the away end - and said they would be working with City to ensure such appalling conduct does not happen in the future.
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