The Brazil international signed for Wolfsburg in August 2013 after failing to establish himself as a first-team regular at Bayern Munich.
Gustavo enjoyed an impressive debut campaign for Dieter Hecking's men, and earned himself a starting place in Brazil's World Cup team.
His performances in Germany's top flight have led to rumours that Real may consider a swoop for his services should Sami Khedira depart the Santiago Bernabeu, while he has previously been linked with Barcelona.
However, a transfer away from Wolfsburg does not appear imminent with Gustavo insisting he is happy to continue at the Volkswagen Arena.
Speaking to Kicker, he said: "I am here, I want to keep playing and help the team here."
Wolfsburg are currently in pre-season training and are gearing up for a DFB-Pokal first-round clash with Darmstadt 98 on August 17, before they open their Bundesliga campaign at defending champions Bayern five days later.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.