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Mueller lasted just ten minutes of Saturday’s 1-0 Bundesliga win at ten-man Hamburg.
He came off the bench at half-time, set up Corentin Tolisso’s winning goal on 52 minutes and then went off injured three minutes later.
“I have a problem with my right hamstring,” he glumly told reporters with a scan on Sunday set to reveal the injury and if the Germany forward will be sidelined.
Bayern face tough back-to-back fixtures against RB Leipzig.
They face RB away on Wednesday in the second round of the German Cup, then host Leipzig on Saturday at the Allianz Arena in a mouth-watering Bundesliga clash.
Bayern are level on 20 points with Bundesliga leaders Borussia Dortmund, but second on goal difference, with RB Leipzig just one point behind in third.
Mueller has been Bayern’s stand-in captain since Manuel Neuer fractured his foot which will keep the Germany goalkeeper out until at least January.
“It wouldn’t be good if Thomas drops out,” admitted Bayern sporting director Hasan Salihamidzic.
There was some good news for Bayern fans on Sunday as Javi Martinez returned to training for the first time since suffering a shoulder injury.
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