Merseyside Police are investigating racist comments posted on social media following the incident between Liverpool's Roberto Firmino and Everton's Mason Holgate in Friday’s FA Cup tie.
The pair were involved in a heated exchange when Firmino reacted to being pushed into the stands by Holgate, and the two players had to be forcibly separated by referee Bobby Madley and their team-mates.
The Football Association confirmed on Saturday it will make enquiries into an allegation made to Madley that arose from the incident between the players.
Merseyside Police confirmed on their official Twitter account on Sunday that they are investigating racist comments made on social media on the day of the match and they are liaising with the two clubs.
"We can confirm we are aware of racist comments posted by a number of individuals on Twitter on January 5, 2018, and will be investigating this," Merseyside Police said.
Deputy chief constable Carl Foulkes added: "We are working with Liverpool FC and Everton FC and hate crime will not be tolerated."
Sky sources understand that Madley will have included the flashpoint between Firmino and Holgate in his match report to the FA and Liverpool have said they will assist in any way they can should further investigation be required.