Voetbal24 says City have made Berge their top target to replace Fernandinho this summer.
The 35-year-old Brazilian is set to leave once his contract expires at the end of the campaign.
Any deal for Berge, 23, would reportedly land old club Genk a 20 per cent cut of the fee after he left the club to sign for United in January of last year.
The Dutchman is wanted by Barcelona when he becomes a free agent in June.
Despite the Blades' imminent drop to the Championship, a deal for Berge would not come cheap.