Sportbuzzer reports Palace have made contact with Wolfsburg about a price for the Holland international.
A move to Palace would mean a return to London for Bruma, who is a former Chelsea youth teamer.
Due to injury, the 26-year-old played in the past season only 13 competitive matches. His contract with the Wolves runs until 2021.
VfL chief Jorge Schmadtke has confirmed "a lot of interest" for Bruma is arriving, "though I have nothing on the table. Once there is, then we can decide".