A report on goal.com said that the German was taking legal action against the Turkish giants over four months of wages he claims are outstanding.
The 25-year-old joined Besiktas on a two-year loan deal last August in a bid to resurrect his career after a catastrophic display in Liverpool's Champions League defeat by Real Madrid.
FIFA "confirmed" it had been contacted by the player, but said it would not comment further as investigations are in progress, according to a spokesman.
Karius has made 26 appearances for Besiktas in all competitions this season, and started their last game on March 10. But has been widely criticised in Istanbul with his head coach Senol Gunes joining in.