The Premier League side are hoping that Zaha will renew his contract and stay at the club.
The Ivory Coast winger is out of contract this summer and is still mulling offers from several clubs.
However, the attacker does give preference to Palace, where he is comfortable.
The appointment of Roy Hodgson for another year is a move that he finds appealing, but he wants to see the club sign promising players as well.
Zaha does not want to spend another season battling relegation.