The 53-year-old man left fighting for his life following an altercation ahead of the Champions League semi-final at Anfield has been named as Sean Cox from Co Meath.
Two men from Rome have been arrested on suspicion of attempted murder.
Mr Cox is being treated for his injuries at Walton Neurological Centre where his condition is described as critical, Merseyside Police said.
Mr Cox is a member of St Peter's GAA Club in Dunboyne and served as chairman of the club from 2013 to 2015. He is listed as the club's Assistant Treasurer on the club's website.
The club released a statement in response to the attack.
"The Club is aware of an incident involving our Club colleague, Sean Cox, at the Champions League game in Anfield last night.
"Sean is a long serving and popular member of St Peter's GAA Club in Dunboyne. At this point we hope that Sean is receiving all of the medical care he requires and that he makes a full and speedy recovery.
"Our thoughts and prayers are with Sean and his family, and we hope that they get the privacy and space they need. We will not be making any further statement at this time."
The 25-year-old and 26-year-old were arrested after police launched an operation to track down the man's assailants amid scenes of violent disorder ahead of Liverpool's clash with Roma.
The Liverpool fan's alleged assailants were among a total of nine men, aged between 20 and 43, who were arrested for various offences before and after the match.
The offences included affray, assault, possession of offensive weapons, possession of a controlled drug, criminal damage and being drunk and disorderly.
Detectives are also investigating the use of flares outside the ground, the force said.
