The France international joined Chelsea from Monaco in 2017 and played an important role in his first season, but was sent to Italy last summer following the arrival of coach Maurizio Sarri and midfielder Jorginho.
Milan have an option to buy the midfielder for €35 million and ex-coach Gennaro Gattuso and director Paolo Maldini said earlier this year that they were keen to make his deal permanent.
However, with three years left on his contract at Stamford Bridge, he is eager to return to London.
The 24-year-old’s brother and agent Abdoulaye says other clubs have already been in touch to discuss a potential summer move, but he would prefer to continue his career with the Europa League winners.
“There are some pretty interesting, quite heavy clubs that have inquired, but we give priority to Chelsea,” he told L’Equipe.
“We already know, there is the Champions League and we are looking for stability, Tiemoue has decided to stay there.”
Bakayoko made 42 appearances in all competitions and scored one goal for Milan as they finished fifth in Serie A, booking a return to the Europa League.
But the former Monaco star had controversial moments in Italy. He was dropped to the bench briefly after turning up late for training and then had an argument with Gattuso on the touchline in May.
Bakayoko was told to get ready to replace the injured Lucas Biglia but television cameras spotted him appearing to tell Gattuso to “f*ck off” after a brief discussion.
He then took to social media to defend himself against the subsequent criticism, saying he “only repeated [Gattuso’s] words”.
Gattuso, who has since left Milan, said that he had put the incident behind him the following day, adding: “I don’t mind if a player tells me to go to hell – the important thing is for him to show respect to his team-mates in the dressing room.
“I have to think about what is best for AC Milan. If the players need to swear at me for the good of the club, then I can deal with that.”