Zaha is on-loan at Palace from Manchester United.
Puncheon told the Mirror: "There is a long-term plan here. There are players here like Dwight (Gayle) and Wilfried who can be the future of the club. I see the club as being one that can continue to grow and I want to be a part of that. We are not just about fighting relegation by any means.
"I'm not surprised by how well we have done since the manager has come in. He is ambitious just like we are."
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