According to Belgian media outlet Het Laatste Nieuws (HLN), the Blades are among a number of clubs – including Borussia Dortmund, Newcastle, Watford, Monaco and Sampdoria – chasing the 22-year-old’s signature.
The fresh speculation comes after it was reported last autumn that United had failed with a '€10m summer bid’ to land Dennis.
He made a name for himself when he scored twice in Club Brugge’s 2-2 draw with Real Madrid at the Bernabeu in the Champions League group stages in October.
The Nigerian international, who has been capped twice by his country, has scored eight goals in all competitions this season and can play as a striker or on either flank.
HLN suggests the Belgian side want €21m for Dennis, who signed a three-year contract in September.