The Dutchman is a key figure for Roy Hodgson's Palace team.
Ajax are likely to lose Nicolas Tagliafico, and if he goes they will look to van Aanholt as his replacement.
The Dutch international is happy at Palace, but his contract runs out next summer, and talks over a new deal have stalled.
If the club can convince him to put pen to paper, a move seems unlikely.
Otherwise, he could be heading to Ajax in the winter.