The Rossoneri have decided to promote the Primavera coach to the full team next season after deciding a move for Unai Emery would prove too costly.
AC Milan are set to replace coach Clarence Seedorf with the Dutchman's former team-mate Filippo Inzaghi, Goal has learned.
The former Netherlands international took over at San Siro in January following the sacking of Massimiliano Allegri and delivered the club to an eighth-placed finish in Serie A.
However, he has not done enough to keep his job after the relationship between coach and board deteriorated during his five-month spell.
Milan have been searching for a replacement, but have been put off their pusuit of Sevilla coach Unai Emery due to the high costs involved.
Club management figures, including owner Silvio Berlusconi and CEO Adriano Galliani, met on Monday afternoon and have decided that Inzaghi is the only viable candidate to train the team next season.
The 40-year-old enjoyed a glittering 11-year spell at the Giuseppe Meazza, winning Serie A and the Champions League twice apiece.
Since his retirement in 2012, he has been in charge of the club's Primavera side and has long been seen as a future coach for the full team.
Berlusconi and Galliani are expected to inform the former Italy of their decision to promote him imminently.