The 22-year-old Germany international forward has been heavily linked with a move away to pastures new in this summer transfer window following two impressive seasons at the Red Bull Arena.
Werner scored 21 Bundesliga goals in 2016-17 to help the side qualify for the Champions League, while he chipped in with 13 this past season - 21 in all competitions - as they finished sixth to book a place in the Europa League.
Liverpool were believed to be leading the chase to sign Werner given that they have already wrapped up a deal to sign his Leipzig team-mate Naby Keita.
However, Milan are also thought to be weighing up a move for the former Stuttgart man but they must wait for UEFA's judgement on Financial Fair Play before they can take the plunge on any big signings.
That would put Liverpool in the driving seat, although Leipzig are said to be keen to keep their star man on board having already lost Keita to the Merseysiders.