The Brazil international is expected to see game time limited at the Allianz Arena in 2013/14 following the summer arrivals of Mario Gotze and Thiago Alcantara.
The 25-year-old operates in a deeper role than the attack-minded signings, but could find it difficult to hold down a spot in Pep Guardiola's plans as competition for places increases.
His possible availability has been noted by Bayern's Bundesliga rivals, with Wolfsburg having already started to put transfer wheels in motion.
Allofs told BILD: "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. There is no doubt about that.
"We are interested in him and we have told his agent about that."
On a possible move away from the current holders of the Bundesliga, German Cup and UEFA Champions League crowns, Gustavo said: "What can I say? I am under contract until June 2015.
"We will have to wait and see how things turn out."