Gazzetta dello Sport (via TalkSport) reported the Rossoneri are eager to add to their options, and the Germany international is on their list.
Football Italia added more details, noting Milan have some financial fair play issues they have to deal with before they can make a move:
The report also stated Leipzig would prefer not to do business at this time, as they will already lose powerful midfielder Naby Keita to the Reds this summer.
Werner is one of the rising stars of German football, scoring frequently for Leipzig and the national team. He won the top scorer's title at the Confederations Cup last summer and is expected to lead the line at the 2018 FIFA World Cup as well.
Known for his blistering speed and natural finishing ability, he would undoubtedly be a great fit in the fast-paced style of manager Jurgen Klopp.
Here is a look at his profile:
Liverpool are not expected to add to their―many―attacking options unless they sell first this summer, but there are some players who could leave. Divock Origi seems a likely candidate after an unsuccessful season on loan at Wolfsburg.
Convincing Werner of the Liverpool project likely wouldn't be hard, but promising him enough minutes is another matter. He has so far prioritised playing time over anything else in his career, opting to join Leipzig from Stuttgart when the club was promoted, at a time it wasn't clear they would be so good in the Bundesliga.
Much will likely depend on the World Cup―if he plays a good tournament, his value will soar, and other clubs might become interested.