La Gazzetta di Modena reports that United boss Sir Alex Ferguson is having scouts watch the youngster in action this season.
The 18-year-old has featured twice and scored on goal for Sassuolo this season.
United are considering making a bid for Berardi, who is seen as one for the future.
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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?