According to The Sun, Arsenal and Tottenham Hotspur are interested in signing Zaha.
Palace chairman Parish, though, has made it clear that there is no plan to sell the 25-year-old former Manchester United winger in the middle of the season.
“That’s out of the question [him leaving],” Parish told BBC Sport about the future of Zaha. "We need to keep going, make sure we get as high as we can up this league.
"Working with Wilf and having Wilf around the club is fantastic. He cares so much about this club.
"He's a joy to work with for every manager, and obviously he makes a big difference to us on the pitch."
Zaha is playing well at the moment and is a key player for Palace, who are in danger of getting relegated to the Championship at the end of the season.
It would make no sense whatsoever for the Eagles to sell such an important player in the middle of the season, even if they are offered £35m in transfer fees.
After all, there is more at stake than £35m, precise staying in the Premier League and the future of Palace.