Werner is viewed at BVB as a replacement for Erling Haaland should he leave at season's end, says BILD.
However, with Werner said to be on a salary of around £17m-a-year, a pay-cut would be necessary for him to move to Westfalenstadion.
Werner did not come off the bench in the 1-0 win against Zenit St Petersburg on Tuesday and has only played nine minutes of club football since Lukaku's return to the club from Inter.
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