The Serie A club's sporting director Walter Sabatini confirmed earlier on Tuesday that the Anfield outfit had expressed an interest in signing the 21-year-old.
Reds boss Brendan Rodgers knows Borini well, having worked with him during their time together at Chelsea and again during a loan spell with Swansea.
Borini netted nine goals in 24 appearances in the league for Roma last season and earned a place in Italy's Euro 2012 squad, although he did not feature during their run to the final.
Agent Marco De Marchi plans to hold further discussions with his client in the coming days as they evaluate the possibility of a switch to the Premier League.
De Marchi told Radio Radio: "Roma has informed us of Liverpool's interest in the boy. Now it's up to Fabio to have his say."
He added on IlSussidiario.net: "We were alerted by Roma of the existence of this deal. I cannot honestly tell you the details but, as Sabatini has already said, we're now seriously considering it.
"Would the player want to go to Liverpool? Honestly, I don't want to commit myself as there will be more news in the coming days. Wait for that."