The highly-rated Ivory Coast international could leave Selhurst Park this summer, with the Toffees readying a £50m offer for the winger, according to Goal, although whether the Toffees will be able to offer that sum if they sign Richarlison remains to be seen.
The 25-year-old has also reportedly turned down a new £120,000-a-week contract in south London due to the player being disappointed with the club's finances and subsequent lack of transfer activity.
However, teammate Ward, who has played alongside Zaha at Selhurst Park for five seasons, has described how important Zaha is to Roy Hodgson's side.
Speaking to the press after Palace's 3-1 over Oxford United - in which Zaha played and scored - Ward said, as quoted by Goal: "We all know how important he is for us and we'd love to keep him and that's what we need.
"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 member of the squad."
"Every time he goes out on the pitch, he does his bit and it's great to have him in the team.
"He just wants to play football and get out on the pitch and show everyone what he can do. He does that pretty much every time he's out there."
Roy Hodgson will hope that Zaha is still a Crystal Palace player when the Premier League season kicks off on 10 August. The Eagles start their top flight campaign a day later with a trip across London to newly-promoted Fulham.