Liverpool have had an extremely busy summer on the transfer front and could be looking to strengthen even further.
The report claims that, despite Klopp's flurry of transfer business throughout the course of the off-season, he is still in the market for a full-back and would love to bring the Italian to the club.
Liverpool manager Jürgen Klopp
Gazzetta Di Parma goes on to report that a fee of around £15-17 million would be required to tempt Milan into selling.
De Sciglio made 29 appearances for the Rossoneri last term and played four games for Italy during their Euro 2016 campaign.
Klopp is reportedly still looking to strengthen his defensive options
The 23-year-old is a wonderfully versatile player and can play on either the right or left side of defence. This would be a fantastic asset for Klopp as his Liverpool side prepare for the physically punishing challenge that is the Premier League.
Reports in the Italian media claim that Milan want to sell certain players in order to re-invest in their playing squad, and De Sciglio is one of those deemed surplus to requirements at the San Siro.
Mattia De Sciglio in action