The Daily Mail reports that United boss David Moyes could splash out on the 20-year-old in a view to replace Rio Ferdinand and Nemanja Vidic.
Maguire recently broke into the England Under 21 rank and is likely to cost United around £4million.
This is set to be the third full season as a first-team regular for Maguire.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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