According to manager Arsene Wenger, the defender is facing a race against time to be well enough to start the match at Signal Iduna Park - adding to Arsenal's defensive woes.
Mathieu Debuchy was carried off on a stretcher with an ankle injury during Saturday's 2-2 Premier League draw with Manchester City, but was set to miss the trip to Germany through suspension.
Wenger also revealed that Nacho Monreal has not travelled with the rest of the squad due to a back problem.
Asked if his side were stretched at the back, Wenger said: "In defence we are, of course.
"The Debuchy injury puts us in a position where we do not want more [injuries] and I hope we have good news after his scan that he will be back soon."
Despite identifying Chambers and Monreal as potential cover, he later confirmed Arsenal could be without both on Tuesday.
"Monreal didn't travel and we have a little problem with Chambers, but he should be alright," he continued.
Wenger hinted there could be an opportunity for youngster Hector Bellerin to step up to the first team.
"We have as well Bellerin, who I think is now ready to play," he added.
"He is not fazed by the pressure and that's an important quality when you're a young boy playing for a big club."
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