The Wolfsburg midfielder, who moved from Bayern Munich in the summer, says he is humbled to be linked with the Catalan giants
The Brazil international moved to the Volkswagen Arena in August, signing a deal running until 2018, while turning down the advances of Arsenal in the process, but has been linked with a swift departure as Barca look to bolster their ranks in defence of their Liga title.
Gustavo is all too familiar with the pressures of playing for an elite club, having joined Wolfsburg from Bayern Munich - for whom he made 100 appearances in two and a half years, winning an unprecedented treble last season.
And the 26-year-old is delighted to have seen his name linked to Camp Nou, revealing he has previously fielded interest from Catalunya.
"It's always good to have your name linked to Barcelona," he told Globo Esporte.
"This is the third time there has been interest from them.
"I have a long contract which includes a buyout fee, and if anyone wants to pay that, they can sign me."
Barca topped La Liga going into the mid-season break, and resume their campaign on January 5 at home to Elche.