The Italians are struggling to return to former glory and want AVB to turn their fortunes around to become a giant of Europe once again.
AVB has had plenty of suitors since being sacked at White Hart Lane, with his record at Porto, Chelsea and Tottenham impressive.
The Portuguese boss paid the price for big defeats to the likes of Manchester City, Liverpool and West Ham this season as well as spending more than £100million in the summer but failing to improve the squad.
The departure of Gareth Bale is looking more costly by the day but AVB is still well respected and is keen to return to management as soon as possible.
West Brom, Cardiff and Rubin Kazan are all expected to contact Villas-Boas over becoming their new manager but the chance to take over at Milan in the summer could be enough for AVB to take six months out of the game.