Allardyce will be looking to stamp his own mark on the Everton squad as he looks to steer them to calmer waters in the Premier League, and he will be given money to spend in the new year.
Former Chelsea star Van Aanholt, who played under Allardyce at Sunderland and then Palace, is now being linked with a move to Goodison Park in January.
Everton are not alone in their interest as runaway league leaders Manchester City are also ready to make a £12m offer, according to reports.
Palace may be willing to offload the six-cap Netherlands international who only made the switch to south London from Sunderland earlier this year in a £9m deal.
Feyenoord striker Nicolai Jorgensen admits missing out on the chance to join Newcastle in January left him frustrated.
Ruben Loftus-Cheek hopes there is enough time left to secure a place in England's World Cup squad after returning to action.
James Tarkowski has credited Sean Dyche for his England call-up, admitting he would have found it 'difficult' to represent Poland.