Having contributed 23 goals in the Bundesliga and Champions league this season, Werner is reportedly wanted by a number of top European clubs.
However, it has been suggested that Liverpool are the frontrunners for the Germany international as Jurgen Klopp considers potential additions before the start of next season.
According to Bild, the Merseyside giants expressed a desire to sign Werner last month, with the intention of loaning the attacker back to his current club for the second half of the campaign.
While a deal never materialised, the proposal is said to have shown that Liverpool are serious about adding Werner to their ranks later in 2020.
Due to a release clause in his contract, the attacker is available for approximately £50m in the summer.