Hansi Flick's side qualified for the Club World Cup after winning the Champions League last season and beat Egyptian side Al Ahly 2-0 in the semifinal.
Bayern last won the tournament in its present guise in 2013, but were also intercontinental champions in 1976 and 2001.
ESPN has contacted local authorities in Bavaria about Muller's possible return to Germany despite an ongoing infection.
The German champions are back in action in the Bundesliga on Monday when they host Arminia Bielefeld, but it is unlikely Muller will feature.
Meanwhile, Bayern CEO Karl-Heinz Rummenigge's suggestion that Bundesliga players should step up and have vaccinations first as it would give people more faith has not been well received in Germany.
"If, for instance a Bayern player receives a vaccination, the trust within the society will grow," Rummenigge said on Sport1 on Tuesday. "Because as a former footballer I know that the body means everything to a pro.
"But we don't want to skip the queue, but as footballers we could do our share for society as role models."
Rummenigge's suggestion was met with widespread criticism as head of the German parliament's Sports Committee Dagmar Freitag suggested selfishness was behind the Bayern chief's proposal.
"It gives you the impression that [Rummenigge] wants to solve his own problems because we know that two of their players could not travel to Qatar because of an infection," she told Sky Germany on Wednesday, adding the background was rather "to have healthy players and not to increase the country's willingness to receive a vaccination."
Sports sociologist Gunter Gebauer, meanwhile, told ARD Sportschau that favouring athletes was "deeply anti-social and morally prohibited, while even several Bundesliga players disagreed with Rummenigge's line of argumentation.
"It is important we don't live in other spheres as footballers" Borussia Dortmund midfielder Thomas Delaney said on Sky Germany on Wednesday. "It would be nice for us, of course. But we also have to wait like all others."
"I can't then go on and say: I want to be vaccinated first. It would not sit well."