BVB are expected to lose Erling Braut Haaland, with the Norwegian having a £67m release clause in his contract this summer.
As a result, the German outfit are likely to be active in the summer transfer market, and according to Sky Deutschland, Werner has emerged as a leading target.
The report adds that the 25-year-old is open to a return to the Bundesliga, although his wages in London would be a problem for Dortmund.
The Germany international has struggled to find his form for the Blues during the 2021-22 campaign, scoring just six goals in 23 appearances in all competitions.
Werner has contributed 18 goals and 17 assists in 75 appearances for Chelsea since arriving from RB Leipzig in July 2020.