LIVERPOOL - AS ROMA SEMI FINAL CHAMPIONS LEAGUE 24/04/2018
Sean Cox, 53, of Dunboyne, County Meath in the Irish Republic is in hospital with a head injury.
Liverpool FC said it was "shocked and appalled" by the incident.
Two men from Rome, aged 20 and 29, have been arrested on suspicion of attempted murder. Seven others are being held for various offences at Tuesday's match.
The attack happened outside The Albert pub in Walton Breck Road, next to Anfield stadium, shortly before kick-off.
Mr Cox has been described as a "long-serving" and "popular" member of the St Peter's Gaelic football club in Dunboyne.
BBC Sport news correspondent David Ornstein said the pre-match trouble started at 19:05 BST when a "group of Roma fans arrived via Venmore Street, burst on to Walton Breck Road and attacked, many using belts".
European football's governing body, Uefa, condemned the events as "vile".
"The perpetrators of this ignominious attack have no place in and around football and we trust they will be dealt with utmost severity by the authorities," it said
"Uefa is waiting to receive full reports before deciding on potential disciplinary charges."