The 20 year-old only moved to VfB last summer and has enjoyed an impressive first season in the Bundesliga.
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Indeed, such has been Chema's impact that he has been likened to Manchester City's Ballon d'Or winner Rodri in Germany.
The Sun says United see Chema as a potential replacement for Casemiro, who will leave Old Trafford when his contract expires in June.
Significantly, Real Madrid have a buy-back clause in Chema's agreement, which they can trigger for £10m.
Chema plays alongside Angelo Stiller in VfB's midfield, with the latter rejecting an approach from United last August.