BILD says new United manager Ralf Rangnick is keen on bringing Werner to Old Trafford.
The pair worked together at RB Leipzig and Rangnick believes he can revive the Germany international's career at United.
A move in January is unlikely, though a summer offer could be made by United on Rangnick's recommendation.
The German signed Werner for RBL in 2016 before he was sold to Chelsea in 2020.
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