Tottenham Hotspur, Everton and West Ham United have all been linked with moves for the Ivorian, who scored nine times and registered five assists in 29 Premier League appearances last term.
Palace are believed to have placed a £70m valuation on the 25-year-old, however, in a bid to scare off interested parties.
Zaha was on the scoresheet in Palace's 3-1 win over Oxford United on Saturday, and Eagles teammate Ward is desperate for the attacker to stay at Selhurst Park.
"We all know how important he is for us and we'd love to keep him and that's what we need," Ward told reporters. "We need Wilf to lead the line of attack and to show what he can do because he has done that time and time again for us and he's a key part of this squad.
"He's a character, he's a winner and he wants to succeed and he wants to win as does every single member of the squad."
Palace will continue their preparations for the 2018-19 campaign with a clash against Stevenage on Tuesday night.