Liverpool say they have substantial evidence relating to Manchester City's claim that a supporter spat at a member of staff, and it could be passed on to police.
The claims overshadowed a thrilling 2-2 draw, live on Sky Sports on Sunday, as City made an official complaint to Liverpool, saying the incident occurred just after the away side's first equaliser.
Although Liverpool are yet to confirm they have identified the alleged perpetrator, they are working with City staff to gather more statements and the unredacted video footage, after analysing footage available to them and collecting a number of statements from supporters in that area of the ground.
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"We are conducting a full investigation, working with all relevant parties including Manchester City, to gather evidence from individuals who witnessed the incident as well as analysing all available video footage," a statement on Monday said.
"The evidence collected to date is substantial and, if requested to do so, will be handed to Merseyside Police given the potential for criminal charges. This case will also be subject to the club's official sanctions process.
"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."
Spitting deliberately at another person can carry criminal charges of assault, and Liverpool could look to ban the individual - if proven - for anything up to a lifetime.
City boss Pep Guardiola said at full-time that he hopes the hosts take action if the claim is proven, but insisted this type of behaviour is "certain people - not just LFC" after referencing the defacing of their team bus at the stadium in 2018.
He told Sky Sports: "I don't know what happened. I heard something from the crowd - something not nice to staff. But I don't know what exactly. I didn't see the images.
"I'm pretty sure that if it happened, what the people told me, I'm sure Liverpool will take measures about this person. Liverpool is much greater than this behaviour.
"Nothing will change my admiration for this club. It was the same story two, three years ago when we came here and they destroyed our bus - it is certain people, not just Liverpool FC.
"It's always a pleasure to come to this stadium. It's an honour for this atmosphere, how they support the team. That's why it's Anfield."