Two men are being sought by police after graffiti reading 'Scab Rats' was scrawled across Liverpool FC's Champion Wall.
Merseyside Police said it received reports of vandalism at around 7.15pm on Tuesday November 30.
The force said graffiti had been left at a number of locations around the club shop end of the stadium.
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The graffiti has since been removed by the club.
The offensive graffiti appeared outside the Reds' home ground just a day before they face Everton in the Merseyside Derby at Goodison Park.
'Tory scabrats' was scrawled on the wall in blue spray paint over the faces of 12,000 Liverpool fans.
Blue spray paint was used to also write 'EFC 1878' under the metal Liverpool crest on another wall surrounding the stadium.
A spokesperson for Merseyside Police said: "Merseyside Police are investigating a report of criminal damage at Anfield stadium.
"At around 7.15pm on Tuesday 30 November, we received a report of graffiti at several locations around the club shop at the Kop end of the stadium.
"It was further reported that two male suspects, one dressed in grey and one dressed in black, left the scene on foot in the direction of the garage on Walton Breck Road.
"The graffiti has now been removed by the club.
"Enquiries are ongoing and anyone who witnessed the incident or has any information is asked to get in touch.
"If you have any information please contact the Merseyside Police social media desk via Twitter @MerPolCC or Facebook Merseyside Police Contact Centre with reference 21000831823.
"You can also call 101 or Crimestoppers, anonymously on 0800 555 111, or their online form at https://crimestoppers-uk.org/give-information/forms/give-information-anonymously "
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