Antonio Conte is a big fan of the Croatian forward and he hopes to lure him to Turin at the end of the current campaign.
Juventus are well equipped in the attacking department, but the boss believes he needs another proven goalscorer for an assault on the Champions League title.
Bayern do not need to sell Mandzukic, but it is believed they will let him leave for a fee of €30 million.
The Bavarians have already agreed to sign Robert Lewandowski from Borussia Dortmund and it is thought the he will be preferred for a place in the starting line-up, meaning the Croat is considering his options.
Mario Mandzukic joined Bayern Munich from Wolfsburg in the summer of 2012 and has since bagged 31 goals in 46 Bundesliga outings, while scoring 5 goals in 16 Champions League fixtures.