A number of Premier League sides were thought to be keen on the Brazilian international over the summer, with Arsenal understood to be leading the chase.
However, the 27-year-old has dismissed the speculation by claiming that he wants to remain with Wolfsburg for the coming years.
"I am very happy. Wolfsburg is a great club to play for and I like living in Germany and the German mentality," he is quoted as saying by Bild. "I feel my future is here and I am able to imagine playing on for many years, because I identify with the city of Wolfsburg."
Gustavo joined Wolfsburg in summer 2013 following a two-year spell with Bayern Munich.