Sky in Italy is reporting that the Serie A giants are anticipating that Liverpool will return with a more acceptable offer for Salah as the two clubs continue negotiations for the 24-year-old.
The same article states that Liverpool have agreed terms with the former Chelsea winger but the Merseyside are still stuck in negotiations with the Italian club.
Salah scored 15 goals and made 11 assists in Serie A last season to finish as one of the division’s most-productive players.
The Egypt international was previously linked with a move to Liverpool before the winger opted to join Chelsea in an £11m deal from Swiss side Basel in 2013 January transfer window.
Salah left the Blues less than six months later via a loan move to Fiorentina before spending the 2015-16 campaign at Roma.
The Serie A runners-up made the deal permanent last summer in a £16m deal and enjoyed a fruitful campaign in the Italian capital.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news