Schalke have drastically dropped their asking price for Kabak after their relegation from Bundesliga.
The Daily Mail says Palace are looking at signing the Turkey centre-back, who spent the second half of last season at Liverpool.
Liverpool had an option to buy Kabak for £18m but declined.
It is believed Kabak could be bought for around £12m.
Leicester and a number of Bundesliga clubs are interested in the 21-year-old.