The Bundesliga giants are looking to sign a new striker, despite having already signed six players over the course of the summer transfer window so far.
However, Kicker report that their chances of signing Mandzukic are 'almost zero', with Juventus unwilling to sell the 32-year-old, with the Croatian set to form arguably the strongest strike partnership in Europe next season, with former Real Madrid star, Cristiano Ronaldo.
Mandzukic scored in the World Cup final on Sunday as Croatia were beaten 4-2 by France, putting in a performance that will have attracted the attention of other top clubs across Europe.
However, the towering striker - who played on the left wing for Juventus last season - recently extended his Juventus contract to 2020, making a move away seem all the more unlikely during this transfer window.
Dortmund are said to have wanted to sign Mandzukic four years ago, but the deal fell through after then-manager Jurgen Klopp decided to pull the plug on the move.
Former Germany international Stefan Effenberg recently told T-Online (via Goal) that he would 'prefer' Mario Mandzukic 'ten times' more than Neymar.
"I never understood why Bayern sold him," he said. "Mandzukic is one of three three best strikers in the world for me. He is working for the team and also scored the goal against England.
"If he were not so old, he would have a market value of €200m. I would prefer him 10 times better than a Neymar."