The 26-year-old has only made 10 appearances for United during the 2019-20 campaign, although he did not make his return from a long-term knee problem until February.
The Ivory Coast international is behind Victor Lindelof and Harry Maguire in the pecking order at Old Trafford, though, and the Red Devils are thought to be keen to sign another centre-back ahead of next season.
According to Gazzetta dello Sport, Milan have been offered the opportunity to sign Bailly this summer, but the Italian giants are not expected to pursue a deal at this stage.
The former Espanyol youngster made 38 appearances for United during his first season at the club but has not featured on more than 18 occasions in any campaign since.
The Ivorian's current deal with Ole Gunnar Solskjaer's side is due to expire in June 2022.