The 27-year-old had been linked with a move to Goodison Park while Sam Allardyce was at the club, with the pair having worked together at Sunderland and Palace, although a possible transfer appeared off following the sacking of the former England manager.
According to the Daily Mail however, the Toffees are still keen to sign the Dutch international despite the departure of Allardyce, believing he could replace 33-year-old Baines - who has recently been linked with a move to the MLS.
A full back known for his attacking capabilities, Van Aanholt enjoyed a fine season helping the Eagles avoid relegation from the Premier League, with his five league goals only bettered by Wilfried Zaha and Luka Milivojevic at the club, while Everton's new director of football and fellow Dutchman Marcel Brands could help push forward a potential move.
Van Aanholt boasts a wealth of Premier League experience, making 126 appearances for the likes of Chelsea, Wigan, Sunderland and Crystal Palace, while a resurgence in club form at Selhurst Park meant a return to the international stage, making his seventh appearance for Holland in a recent friendly against England.
Should Van Aanholt move to the blue half of Mersyside, he could be working under a new face at the club, as Everton appear set to announce the appointment of former Hull City and Watford boss Marco Silva as their new manager.