Die Wolfe are chasing the Bayern Munich midfielder and see the Brazil international as an ideal addition to the squad this summer
Die Roten signed Thiago Alcantara from Barcelona for €20 million [£17.2m], adding even more competition to the already packed midfield at Sabener Strasse.
Aware that Luiz Gustavo's first-team appearances could suffer, Alloffs is keen to lure the Brazilian to the ambitious Niedersachsen outfit.
"When the speculations about Bayern having too many midfielders came up, we said that Luiz Gustavo would be a player who'd fit us very well in terms of his quality," Alloffs told SID.
"However, initially there are a lot of obstacles standing in a way in order to complete a deal. We already talked to his agent and informed Bayern about our interest, but so far, that's all."
Meanwhile, coach Dieter Hecking confirmed that die Wolfe have begun chasing for the 26-year-old's signature but admits they are still far away from reaching an agreement.
"We have told Bayern about our interest in Gustavo," Hecking said. "However, I'm a coach and a realist. First and foremost, Bayern would have to talk to the player and they can always say that he's going to stay."
Gustavo arrived at the Allianz Arena in 2011, but has since struggled to establish himself as a regular, first-team player.