Gomez has hit 12 goals in the first 11 games. Muller holds the record with 40 goals in the 1971/72 season.
Gomez, who also hit a hat-trick in 25 minutes in the Champions League against Napoli on Wednesday, will fancy his chances of adding to his haul when the Bundesliga leaders meet Augsburg on Saturday.
Augsburg, in 17th place and a point above last-placed Freiburg, look like the perfect punch bag for the 26-year-old Gomez with the promoted Bavarian team having managed only one win so far.
Bayern have scored 30 league goals and conceded just three as they lead the standings four points ahead of Schalke 04.
"No doubt about it, I am confident Mario can break my record," former Bayern and Germany great Muller has said.
The signs are good for Gomez but the Germany forward wants to hear none of it.
"This is just for the public," Gomez told reporters on Thursday. "What matters and what remains are the titles you win with a team. League and Cup, that's what matters.
"Obviously I am happy but at the end of the day scoring goals is my job."
He is only the second Bundesliga player in 27 years to have scored 12 or more goals in the opening 11 games with Vedad Ibisevic having netted 13 times in Hoffenheim's Bundesliga debut season in 2008/09 before injuring himself and missing the rest of that season.
Second-placed Schalke, on 21 points, have their own prolific scorer in Klaas-Jan Huntelaar with 10 goals so far.
They travel to Hannover 96 on Sunday hoping the Dutchman, who has reportedly generated interest from major European Clubs, will again be on target to keep them on Bayern's tail.
Champions Borussia Dortmund, a further point adrift, also tasted Champions League victory on Tuesday against Olympiakos Piraeus and will be looking to beat VfL Wolfsburg for their fifth win in the last six league games.
