The Rossoneri are reportedly offering €3 million up front to secure Bakayoko for at least the 2020-21 season.
The 25-year-old excelled while on loan at Milan during the 2018-19 campaign, but the club declined to make the move permanent. Bakayoko was reprimanded for swearing at then-manager Gennaro Gattuso during a Serie A match and for showing up late to training.
He spent the past season at AS Monaco, where Bakayoko first shot to prominence with Leonardo Jardim's title-winning side in 2016-17. Bakayoko made 20 starts in Ligue 1 before the coronavirus pandemic forced the season to be abandoned.
A defensive midfielder with superb dribbling ability, Bakayoko could offer Milan some much-needed depth. Stefano Pioli is currently looking for players to replace Lucas Biglia and Giacomo Bonaventura, whose contracts expired at the end of the campaign.