Reds' youngster Jordan Rossiter, out of contract in June, is being targeted by the Italian side.
Rossiter, tipped by many involved with Liverpool as having the potential to become the natural successor to Steven Gerrard, has made just five appearances for the Anfield club's senior side.
However, when given chances he has shown signs of possessing the raw talent and potential to be a midfield star of the future, scoring a fine long-range effort on his first-team debut last season against Middlesbrough in the Capital One Cup.
He was handed a Premier League debut by former manager Brendan Rodgers at the start of the current campaign, and although his development was somewhat hindered by an injury absence he has also featured under Jurgen Klopp.
As Rossiter is only 19, Liverpool would be entitled to a compensation fee if he joins another club, although the Star claims this is only likely to be around £250,000.
Losing the England Under-19 international, highly regarded as one of the most promising players in the club's academy, would be a blow for the Reds as they look to continue their record of nurturing developing talent for the first team.
Gerrard is one of the most prestigious graduates of the club's academy in recent times, but current first-team players Jon Flanagan and Brad Smith have also progressed through the ranks in recent years.