The Mirror reports that United boss David Moyes watched the 22-year-old in Belgium’s victory over Scotland on Friday.
Moyes is reportedly interested in adding more height and strength to his striking options.
Villa handed Benteke a new £60,000-a-week contract in July after the striker asked to leave the club.
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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.
Who of Europe’s top strikers will move to England this summer?