The Reds have been active in the transfer market so far this summer, with Jurgen Klopp having overseen six deals in his first off-season on Merseyside.
Although there have been numerous signings and problems in goal and midfield have been somewhat addressed, the Anfield side are short on both sides at full-back, and reports claim De Sciglio could be signed in response to this.
The 26-cap Italy international is a ostensibly a right-back, but through his career he has filled in on the left side of Milan’s backline, so he could provide back-up for Nathaniel Clyne and Alberto Moreno at Liverpool.
The Rossoneri will demand around £16.9m for their man.
The 23-year-old has made 106 appearances for Milan since gradating from their youth ranks.