The 26-year-old forward joined Bayern from Stuttgart in 2009 and has since developed into a key player for the Bundesliga giants.
Gomez has a contract with Bavarians until the end of next season, but the striker is keen to stay at the Allianz Arena beyond his current deal.
“Mario is very happy in Munich. That is why we have never been involved with other clubs,” Gomez’s agent, Uli Ferber, told Sport Bild.
“There is therefore no objection to a contract extension – we have no time constraints.”
Gomez has already netted 22 goals in 25 Bundesliga appearances during the current campaign.
Meanwhile, Bayern are believed to be keeping tabs on Werder Bremen attacker Claudio Pizarro as they are preparing for life after Ivica Olic.
Olic is expected to leave Bayern on a free transfer this summer, and they regard the 33-year-old Pizarro to be the perfect replacement.