There are also reports about him being unhappy with arguments with the coach and some players during the Champions League final loss to Real Madrid in June in Cardiff.
It is believed that Allegri was unhappy with the discipline shown by the 30-year-old defender, which is why he has made a decision to let go of him, along with Dani Alves.
Bonucci will now undergo his medical and put pen-to-paper on a contract with Milan to become their ninth new arrival this summer as the Italian giants continue to build a formidable new squad.
Bonucci was heavily linked with a move to Manchester City last season but it didn't materialize due to the 30-year-old's unwillingness to leave Italy.
Bonucci, who started his career at Inter, has chose to remain in Serie A and is expected to sign a contract that ties him to the San Siro club until 2022.
Southampton defender Virgil van Dijk is reportedly on their radar, but the club have looked towards Germany initially to get a replacement for the AC Milan bound Italy worldwide. "There are times when you should turn a blind eye and times when you have to have your eyes wide open and in that moment Leo was wrong", he was quoted as saying by the Daily Mail.
Bonucci's move is certainly a surprising one but the defender should help to make Milan more resolute at the back.
AC Milan have spent wisely this summer but heavily as they attempt to take the Serie A by storm next season.
The deal could go through for as little as £35m with Juventus happy to give Bonucci every chance of a new start after seven years at the club.