One of the complaints follows an alleged racist remark directed at Senagalese striker Demba Ba who scored the opening goal of Chelsea's 2-0 win.
According to the Liverpool Echo, it is not known whether Ba heard the alleged remark.
The newspaper also reported that Liverpool are aware of the allegation, and it is believed 'the incident' was conveyed to the anti-racism body Kick It Out by a Reds' fan.
A police spokesman told the Echo: "Merseyside Police can confirm that officers are aware of an allegation that potentially racist comments were directed towards two players during the match between Liverpool and Chelsea.
"No report or formal complaint has been received by the force at this time. Enquiries are being made into the circumstances surrounding the allegation."
Four arrests were made after the match following a number of skirmishes between rival fans.
Police will watch CCTV footage in an attempt to identify those involved in the clashes.