The Danish striker is on his way out of Arsenal this summer and is believed to be considering offers from a number of clubs.
However, Bruchhagen has all but ruled the Eagles out of the running, claiming that they cannot afford to meet the 25-year-old's wage demands.
"Chances are slim that Nicklas Bendtner will be joining us," he told Die Welt.
"He is simply in a different salary class and even if we would be able to pay those wages, he cannot deceive our key players."
Bendtner spent last season on loan at Juventus, where he made just two league starts.