Liverpool have been strongly linked with the Italy international ever since the appointment of Brendan Rodgers, who managed Borini for a loan spell at Swansea.
He scored six goals in nine games after joining the then Championship club from Chelsea in March 2011 and subsequently returned to Italy on a free transfer, scoring nine times in 24 Serie A appearances for Roma in the 2011-12 campaign.
Having said on Monday that an "exciting" deal could be completed this week, Rodgers is now looking to bring Borini to Anfield, according to Roma.
“There is real interest in Liverpool for Borini,” Sabatini said.
“We are evaluating things with Roma director general Franco Baldini and the club, if necessary, will act accordingly.”
Borini travelled to Euro 2012 as a member of the Italy squad but did not make an appearance in Poland and Ukraine.
Liverpool could make room in their squad for the striker by loaning Andy Carroll. Rodgers has said the club are potentially open to allowing the £35 million signing to leave Anfield on a temporary basis.