"I can well imagine myself staying at Munich beyond 2013. I feel good here and - in the sporting sense - things are going well," said Gomez, 26.
Sport Bild hinted negotiations for a new deal could start next month.
Bayern CEO Karl-Heinz Rummenigge said, however, that a decision would not be made before December.
Gomez topped the Bundesliga scoring charts last season with 28 goals and this season has already bagged eight in just six games to help take Bayern top of the table.