But Parish plans to sit down the 23-year-old at the end of the season to discuss a new contract and is confident of persuading him to stay.
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Wilfried Zaha has been key for Crystal Palace this season
Zaha has been Crystal Palace's star man this campaign, scoring six goals and providing 11 assists.
"It will be really hard for him to go in the summer, really difficult," Parish told Sky Sports.
"We're confident [he will stay]. Wilfried is focused on the end of the season and keeping us in the division.
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Steve Parish to sit down with Wilfried Zaha at the end of the season
"He's been here since he was very young. We'll sit down at the end of the season and I'm very confident we can keep him.
"We want to go up the league. We thought the season would have gone better than it has turned out but we still have the chance to finish relatively high.
"I think we're only three or four points off 10th. We're looking to improve the squad and improve the squad and Wilfried is an intrinsic part of what we're doing."
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