Various price tags have been mooted for the Ivory Coast international.
He is tied to a contract through to 2023 that was only signed last summer, so his current club are under no pressure to sell.
As a result, Palace are in a position to demand whatever they want for a prized asset.
A fee of around £60 million has been suggested as the mark which may tempt those at Selhurst Park into transfer talks for a player who has expressed a desire to move on.
Palace chairman Steve Parish is not ruling out a sale heading towards the next window, but neither is he prepared to bow to the demands of player or rivals.
“There is a perception with Palace that people can just come along and pay less than market value for our players. That just isn’t going to happen.”
Parish added on a player who has rebuilt his reputation since returning to Palace from a forgettable stint at Manchester United: “I don’t want Wilf to leave. We want to progress and the best way of doing that is Wilf in our team.
“At the same time, I know you can get boxed into a corner over these things — but he is on a long contract.”
Zaha was, after an initial loan spell, re-signed by Palace in February 2015.
He has starred for the club over recent years, with a personal-best return of 10 goals recorded in the 2018-19 campaign.
That contribution helped Roy Hodgson’s side to a 12th-place finish, with the club comfortably consolidating their top-flight standing once more.
Hodgson himself addressed the future of Zaha and other Palace stars, like Aaron Wan-Bissaka, after the Eagles final Premier League game.
“There’s nobody at the club who’s anxious to see any of those players leave the club, in fact it’s the reverse. We’ve committed them to long-term contracts,” the former England manager said.