At face value, the Croatia international would be a perfect signing for BVB; perhaps as good as the club could ask for in the current market. Mandzukic is a monster, physically speaking; his sheer athleticism would suit Juergen Klopp's pressing system to a T.
Like Lewandowski, the Croat is incredibly tenacious; he drops back to defend even in his own penalty box and will chase down defenders, giving them little to no time on the ball. The difference is, he's even larger and better in the air.
At the attacking end, Mandzukic is not as prolific as Lewandowski. But that has been no problem at a Bayern team that gets goals from midfield at a staggering rate. Dortmund have scoring options in midfield as well, including Marco Reus, Pierre-Emerick Aubameyang and Henrikh Mkhitaryan, plus the possibility of signings like Shinji Kagawa and Kevin Volland.
Just as he's mastered the art of frustrating defenders and making space for his teammates at Bayern, so could Mandzukic do the same at BVB. He'd also be a great asset from set pieces, an area in which Lewandowski has not exactly impressed: The 1.87-meter man has scored as many goals with his head—seven—this season as he has with both feet combined. And critically, he'd be hungry to prove himself against a Bayern team that believed he was not enough in the striker position.
Yet, as great as Mandzukic would be for Dortmund, Klopp and company would be unwise to pursue him in the transfer market.
The first reason is a matter of feasibility. Dortmund are well aware of Bayern's ruthless transfer market strategy, and the Bavarians would surely rather sell to a foreign club or even let Mandzukic warm the bench and collect his €5.5 million per season than relinquish him to BVB. After all, Dortmund took a similar stance on Lewandowski, forcing the player to honor his contract. To make any serious effort to sign Mandzukic would, in most likelihood, be a humiliating waste.
Even if Dortmund were able to sign Mandzukic, the message such a purchase would send is extremely destructive to the club's image. With due respect to the Croat, Lewandowski is overall the better striker. The Pole is two years younger, but scored as many goals as Mandzukic in 2010-11 (the first season for each in the Bundesliga) and has since outscored his counterpart in each season until the present. If Dortmund were to sign Mandzukic, they would have swapped Lewandowski and €25 million in exchange for a player of lesser value than the Pole.
Moreover, such a transfer would only further enforce the Soviet-esque narrative that everything in the Bundesliga belongs to Bayern, and that other clubs can have only as much as Bayern allow them to have. Playing into such a narrative is not becoming of a club that has ambition, and current players and prospective signings would surely consider that as they mull contract offers.
Dortmund instead need to look elsewhere for an impact player. The club cannot afford to rely on a player who struggles to score and needs time to develop: they did that with Lewandowski in 2011-12 and, although he scored 35 goals in all competitions for club and country that season, BVB were eliminated from the Champions League by mid-season.
Unready for competition at the very highest level, the Pole scored just once in six group stage fixtures. Such is natural for a developing player, and a rising talent like 19-year-old Anderlecht forward Aleksandar Mitrovic or 20-year-old Liege striker Michy Batshuayi are not exactly the right solution. Such a player is ideal to have on staff for the future, but it's unfair and unwise to put such pressure on a young player's shoulders.
Eliminating the rising stars and those who may be out of BVB's reach financially leaves few options, but Dortmund's scouts are world-class and the club remains a highly desirable destination. Mandzukic may be a clearly evident option, but BVB would be wise to choose the prudent over the obvious.