Il Corriere Dello Sport claims the Serie A club have made the Serbian defender a major summer target as AC Milan look to life without Paolo Maldini at the end of the season.
Carlo Ancelotti, AC Milan's coach, is understood to be keen on Vidic partnering Brazilian defender Thiago Silva.
However, any deal could hinge on the club playing Champions League football next season. AC Milan currently lie third in Serie A, two points ahead of Fiorentina.
Meanwhile, former Manchester United player David Beckham flew to Qatar with the rest of the AC Milan squad for their friendly against Al Sadd in Doha.
Beckham, currently on-loan at the San Siro, said that he still harbours a desire to stay with the Italian club.
An agreement would allow Beckham to finish the Italian season with Milan before joining LA Galaxy in July. A deal is finally expected to be completed this week.