At 31, Mueller proved he is in his prime with a Bundesliga record 21 assists last season, serving as the perfect foil to Bayern striker Robert Lewandowski.
The pair will be hunting more goals at home to Red Bull Salzburg on Wednesday as Bayern chase their 15th straight win in Europe and a fourth victory from four games in Group A.
Mueller created two goals and Lewandowski netted twice in a 6-2 win at Salzburg earlier this month.
Yet in the wake of Germany's record 6-0 defeat by Spain last week, pundits and former players insist Mueller can provide the impulse the national team is lacking.
With five Bayern teammates in the Germany side routed in Seville, Mueller admitted the debacle made painful viewing.
"Of course, you suffer along with your fellow players in the club and former national team colleagues as much as the fans," he said after Saturday's 1-1 draw against Werder Bremen.
"German football fans long for things to go well again.
"At the moment there is a lot of negativity around the topic, it hurts, but my main focus is on the club."
In March 2019, Germany coach Joachim Loew told Mueller and fellow 2014 World Cup winners Mats Hummels and Jerome Boateng that their international careers were over.
Now, Bastian Schweinsteiger is leading the calls for his former Bayern team-mates to be reinstated before the European Championship starts next June.
"Such players like Jerome Boateng and Thomas Mueller have won the treble with the best team in Europe," said Schweinsteiger.
"They are first choice, have the quality and are German players - why are they not in the national team?"
As Mueller points out, "none of us (him, Hummels and Boateng) have retired" from Germany duty, "but after a 6-0 defeat like that, we should be talking about other things."
For now, Mueller is letting his performances this season do the talking with eight assists and six goals in Bayern's 14 games.
Germany's loss is Bayern's gain, as far as coach Hansi Flick is concerned.
"He's got a very good sense of the game tactically and is very important on the pitch – he's the coach's right-hand man," Flick said.
"He leads the team and plays at a very high level. Thomas is a player that would do any team good."
When Flick replaced Niko Kovac in November 2019, he immediately reinstated Mueller from the bench to the starting line-up.
It was a key switch as Bayern swept aside all rivals on their way to lifting the Champions League trophy and an eighth straight Bundesliga title.
Mueller has spent his entire career at one club, a rarity in modern football.
He won the free-kick which David Alaba blasted home in a 3-2 win at Dortmund earlier this month as Mueller broke Oliver Kahn's record of 260 league victories for Bayern.
Mueller "has been shaping" Bayern "for more than ten years with great football", Kahn said earlier this year.