The Welsh star's performances at Euro 2016 have allegedly caught the eye of the Serie A side.
The Welshman looks set to depart Anfield this summer after falling down the pecking order at the club.
Last season he saw his game time limited as manager Jurgen Klopp favoured Emre Can, Jordan Henderson and James Milner in the centre of midfield.
That has led to suggestions that he will leave this summer to seek first-team football elsewhere so as to avoid his career stagnating on Merseyside.
He is currently at Euro 2016 with Wales, where he has played a key part in their impressive run to the semi-final stage of the competition.
That has attracted interest from several clubs across Europe, and according to the Daily Mail Inter Milan are one of those who could make a move in due course.
However, it remains to be seen whether the Italian side would be willing to pay Liverpool’s asking price for the midfielder.