A 53-year-old was critically injured after being attacked by the two men, both of whom are from Rome, at the Albert Pub, which resides close to Anfield's Top Stand.
Detective Inspector Paul Speight said: "We believe the victim was in Liverpool with his brother for the Liverpool v Roma semi-final and was assaulted during an altercation between Roma and Liverpool fans near to the Albert pub at about 7.35pm.
"Witnesses report that the victim was hit with a belt and then fell to the ground. Paramedics treated him at the scene and he was taken by ambulance to Walton Neurological Centre, where he is being treated for a head injury. His condition is currently described as critical and his next of kin have been informed.
"The place where this incident occurred is right by the ground and was heaving with fans making their way to the game. I would appeal to anyone who has any information, or mobile phone footage of the incident, to contact us urgently, as information they have could be vital to our investigation."