Police say the attack happened at 19:35 BST, ten minutes before kickoff, outside the Albert - a well known watering hole for Liverpool fans.
About 80 Roma fans are through to have used a side road to reach the Liverpool fans, and there is footage of one fan outside Anfield with a hammer.
"Roma fans have just attacked Liverpool supporters with belts, outside the Albert. One guy down getting treatment," said Sunday Times correspondent, Jonathan Northcroft.
"The Roma group came out of Venmore Street, and attack was sudden.
24 April 2018
He added: "Roma group were chased down the street before police arrived."
Police are appealing for anyone with video footage or information to contact them.
24 April 2018
This comes after an increased security presence was needed following the ugly scenes before the quarter-final tie against Manchester City in the previous round.