The 20-year-old has quickly become a regular for the Bundesliga side but has been unable to prevent Schalke's slump to the bottom of the table this term.
Schalke are currently seven points adrift of safety in the German top flight, and Kabak is expected to leave if the Royal Blues drop down to the second tier.
Man United, Liverpool and AC Milan have all been credited with an interest in the Turkey international, and the Daily Mail now claims that Crystal Palace are also in the running as Roy Hodgson plots a defensive overhaul.
The report claims that the Eagles boss is keen to ship out Mamadou Sakho and James Tomkins in the near future, while Scott Dann and Gary Cahill's time at Selhurst Park is almost up as they approach the latter stages of their careers.
Kabak, who is said to be valued at £25m by Schalke, is under contract at the Veltins-Arena until the end of the 2023-24 season.