Bonucci shocked Juventus in the summer when he decided to leave the club for fellow Serie A rivals Milan.
After guiding Juve to another league title, he made the 42million euros switch to Milan and has since played 10 games in the league.
Reports in the summer claim he clashed with Allegri and his handling of team affairs but Marotta has moved to deny those rumours.
When asked, he told Il Giornale: "I want to point out that Bonucci did not leave because of Allegri.
"He was not the cause. We were already prepared, because in the discussions a club normally has with its players, Bonucci had expressed dissatisfaction."