Low's men face England on Tuesday at Wembley, an encounter that comes just four days before Bayern's top-of-the-table Bundesliga clash with Dortmund, while they will travel to Russia to meet CSKA Moscow in the UEFA Champions League next Tuesday.
Dortmund goalkeeper Roman Weidenfeller is poised to make his international debut, while his club-mates Sven Bender and Marco Reus could also feature.
By contrast, Bayern shot-stopper Manuel Neuer and captain Philipp Lahm are set to be rested, a decision that some have suggested is unfair on Dortmund ahead of their crucial clash at Signal Iduna Park.
But, while Low accepted that criticism, the Germany coach was quick to defend his selections.
"Absolutely (it is unfair), but we have six months until the World Cup," he said.
"I need those tests and Dortmund v Bayern is not my province.
"Ask the players, they all want to play. Neither (Dortmund coach Jurgen) Klopp nor (Bayern boss Pep) Guardiola would dictate to me but to be honest it isn't that important to me.
"The same player will not play both 90 minutes but it is a media issue. (They are) adding oil to the fire.
"There is no way these guys are overstretched from playing twice in four days."
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