Reports emerged of violence between the two sets of fans shortly before kick-off at Anfield, as Liverpool went on to win the semi-final first leg 5-2.
Merseyside Police confirmed the force was investigating a "serious assault" of a man outside The Albert pub, located close to Anfield on Walton Breck Road.
After making a social media appeal for information, Merseyside Police confirmed the arrests of two men from Rome, aged 25 and 26, in connection with the incident.
The victim, a 53-year-old man said to be a Liverpool fan, suffered a head injury and was taken to a local hospital in a critical condition.
UEFA slammed the attack as "vile", but will wait until "full reports" have been received before deciding to take any action themselves.
"UEFA is deeply shocked by the vile attack that occurred ahead of the Liverpool FC v AS Roma match and our thoughts are with the victim and his family," a statement from the governing body read.
"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.
"UEFA is waiting to receive full reports before deciding on potential disciplinary charges."
After Liverpool expressed their shock in the wake of the attack, the Italian club have also released a statement, saying: "Roma condemns in the strongest possible terms the abhorrent behavior of a small minority of traveling fans who brought shame on the club and the vast majority of Roma’s well-behaved supporters at Anfield after getting involved in clashes with Liverpool supporters before last night’s fixture.
"There is no place for this type of vile behavior in football and the club is now cooperating with Liverpool Football Club, UEFA and the authorities.
"The club’s thoughts and prayers are with the 53-year-old Liverpool fan in hospital and his family at this time."