The youngster left Sunderland for Dortmund over the summer, but is unsettled in Germany.
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Bellingham has struggled to find a place in BVB coach Niko Kovac's XI, which sparked a row with his father, Mark Bellingham, earlier this season.
A move away from January is now being considered and BILD says United are interested.
Also keeping tabs on the situation are Crystal Palace, which see Bellingham as a potential replacement for Adam Wharton, who ironically, is a target for United.