And they have told any prospective new owners that the Ivorian will be at the club next season.
Zaha is determined to force through a move this summer and has asked Palace to let him join Arsenal before the August 8 transfer deadline.
But chairman Steve Parish thinks letting the winger leave could scupper his ambition to sell the south London club in the future, according to the Sun.
Palace have already sold Aaron Wan-Bissaka to Manchester United this summer for a whopping £50m.
In turn, they have slapped an £80m price tag on Zaha in the hope it will put off any potential suitors.
Palace are said to be in talks with Chinese suitors over a potential £220m takeover.
American investors Josh Harris and David Blitzer are ready to be bought out, while any new owners would have to clear some of the debt at Selhurst Park.
Parish has a long-term vision for the club, which is why he feels so strongly about keeping Zaha this summer.
Arsenal, meanwhile, need to sell players to raise funds for Zaha and other transfer options.
Unai Emery has a budget of around £45m, meaning the Spaniard will be forced to sell players to land his top targets.
Yannick Carrasco, Ryan, Fraser, William Saliba, Kieran Tierney and Julian Weigl have all been linked with moves to the Emirates.
Nacho Monreal, Laurent Koscielny and Calum Chambers are all expected to leave this summer to make room for Emery’s new arrivals.
The trio are unlikely to be sold for significant transfer fees but will certainly help trim the wage budget in north London.
Monreal is likely to make way for Tierney, who will leave Celtic should they receive a bid of around £20m.
Koscielny is being eyed by a number of Ligue 1 sides, notably Lyon and Rennes.
While Calum Chambers has failed to live up to the hype after his move from Southampton.
The defender has been tentatively linked with Serie A outfit Lazio.