Since the turn of the year, United have been heavily linked with Grealish, who has been the star man in a struggling Villa side this season.
However, according to the Evening Standard, the North-West outfit will only pursue a deal for the 24-year-old if they can get Pogba off their books.
While Ole Gunnar Solskjaer has consistently stated that the World Cup winner has a future at Old Trafford, reports continue to indicate that United would welcome a sale.
Pogba, who effectively has just over two years left on his contract, has been restricted to just eight appearances this campaign due to injury.
Real Madrid and Juventus have frequently been credited with an interest in the France international.