While Fabian Delph continues to do a fine job on the left flank for City, Guardiola still wants to bring in a specialist as cover for Mendy, who is recovering from a knee injury suffered against the Eagles in September.
The Spanish tactician has identified Van Aanholt as that specialist and believes he could persuade Roy Hodgson to sell in January.
Palace already have Jeffrey Schlupp and Joel Ward in the left-back position, meaning the club could sell to raise funds to strengthen other areas in the new year.
It is understood that City are also monitoring Southampton's Ryan Bertrand and Espanyol's Aaron Martin.