The Wolves are looking to sign the Brazilian to beef up their midfield for an assault on a place in Europe next season, while the 26-year-old may also find his first-team opportunities limited at Bayern this season given the arrivals of Thiago Alcantara and Mario Gotze.
His contract with Bayern still has two years left to run on it, but Wolfsburg should have no problems stumping up a fee for the former Hoffenheim player's services.
"We've made contact and expressed our interest," said Wolfsburg's director of sport Klaus Allofs to the Bild newspaper.
"We want to do things correctly. There are still some obstacles to overcome, however."
Gustavo has been included in the Bayern squad for today's Supercup against Borussia Dortmund, although he is not expected to figure having yet to feature under new Bayern coach Pep Guardiola since returning from the Confederations Cup.