The report adds that Palace are willing to accept an offer of around £65m for the 26-year-old player.
Everton have already signed Moise Kean from Juventus and if they manage to land Zaha, they will have the best attack outside of the top six.
His departure will be a massive blow for the London side but his decision is understandable. Zaha is good enough to play for a side challenging for Europe.