The Brazilian midfielder has seen his place in the Bayern side called into question following the summer arrivals of Mario Gotze and Thiago Alcantara.
It is difficult to see how Pep Guardiola is going to fit the wealth of talent he has at his disposal into a starting XI, and keep everyone happy over the course of the 2013/14 campaign.
The potential availability of Gustavo has been noted at Wolfsburg, who have admitted to holding an interest, while Arsenal have also been linked with an imminent approach.
Gustavo is aware that his future has become the subject of much conjecture, but the 26-year-old says he has not sparked the rumours and would be happy to remain at the Allianz Arena.
A man who helped Bayern to an historic Treble last season told Deutsche Presseagentur: "I want to stay on at Bayern Munich.
"I am under contract with the club and I want to fulfil that commitment.
"I have been in a position to fight for a first team role throughout my career. I will keep on fighting this year, too."