Liverpool have collected "substantial evidence" after Manchester City made a complaint alleging a home fan spat at their backroom staff in the first half of the 2-2 draw at Anfield on Sunday.
Liverpool are conducting a full investigation into the incident.
In a statement the club said witnesses had been interviewed while CCTV and video footage was being analysed.
"The evidence collected to date is substantial," Liverpool said.
"If requested to do so, [the evidence] will be handed to Merseyside Police given the potential for criminal charges."
It is understood any Liverpool fan found to have spat at Manchester City staff would face a possible lifetime ban from Anfield.
In a thrilling game on Merseyside, City twice came from behind to claim a point, with Kevin de Bruyne levelling the second time after Mohamed Salah's superb solo goal had again put the Reds ahead.
It was not without on-field controversy, with Pep Guardiola furiously remonstrating with officials after James Milner did not receive the second yellow card the City boss felt the Reds full-back's foul on Bernardo Silva deserved.
Liverpool added in the statement: "Anfield is our home and we will ensure it is a safe, enjoyable environment for everyone attending and will not allow unacceptable isolated behaviour to impact on our club's values and principles."
The draw leaves City third in the table on 14 points, a point and a place worse off than Liverpool and two points behind leaders Chelsea.
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