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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.