Sam Allardyce's side, who currently occupy the 16th spot in the table and are six points clear of the drop zone, have relied hugely on both players in the recent days.
Zaha has been the best creative player for the Eagles this season while Liverpool loanee Sakho has played a key role in steadying Palace's defence in the second half of the season.
Club chairperson Steve Parish said: "We'll sit down and talk to Wilf when we're mathematically safe."
"He has four years to run so the question about whether he will be leaving is nonsense."
"We've not had any offers. Everyone wants him to stay, he wants to stay. Sakho? That's a tougher one, he was at this game and didn't have to be."
"It takes two sides to make a deal and if we can do something sensible we will."
"We've broken all our transfer records, we topped the money league in January and can't do that. We need to be sensible. The player has put himself in the shop window and we will just have to see how that pans out."