According to the Daily Express, Arsenal and Spurs have both keeping tabs on the 26-year-old Brazil international, who is expected to feature for his country at the World Cup on home soil this summer.
And speaking to FIFA.com, Gustavo confirmed that he is happy playing his football in the Bundesliga, all but ruling out a move to Arsenal, Tottenham or even Barcelona.
"It's aways nice when the top clubs are interested in you," Gustavo told FIFA.com. "But right now I'm here and I'm very happy.
"The Bundesliga has become even better known in Brazil thanks to Bayern [Munich]."
Gustavo was linked with Arsenal and Tottenham last summer when it became clear he was ready to leave Bayern Munich for first-team football.
But he eventually decided to stay in Germany because he believes the Bundesliga is one of the best places to play football.
"Here every stadium is always full and the league is strong," Gustavo continued. "I think she is the best league in the world."
The Brazil midfielder left Bayern Munich after two years at the club, but he insists he made the right decision to move on when he did.
"New challenges are always good," said Gustavo. "Perhaps that is the story of my life. I always had to move on to achieve something so I always look forward to a new challenge."
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