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.