The Brazilian midfielder has fallen out of favour at Bayern Munich over the last year and sporting director Klaus Allofs is hoping to lure him away from the club
The Brazil international has found himself out of the Bavarians' first-choice XI since the arrival of Javi Martinez last summer and has further competition for a midfield berth after the club signed Thiago Alcantara.
And the Volkswagen Arena outfit are set to offer him a route out of the Allianz Arena ahead of the 2013-14 campaign.
"If you are looking to improve your team, and if the player is available for transfer, you have to discuss the name of Luiz Gustavo," he told Bild.
"There is no doubt about that. We are interested in him and we have told his agent about that."
However, Gustavo has moved to deny he had heard from any suitors but hinted he could be tempted to leave his current employers.
"I know nothing of the rumours," he said. "No one has spoken to me. We have to wait and see what happens now."The 25-year-old first moved to the Allianz Arena from Hoffenheim back in January 2011 for a fee of €17 million. His contract expires in 2015.