The 19-year-old has been in impressive form for Ian Holloway’s side this season, scoring five goals in 25 appearances in the Championship as Palace look to secure promotion to the top flight.
Zaha made his senior England debut in a 4-2 defeat by Sweden in October and the winger recently expressed his desire to leave Selhurst Park and move to a Premier League club in the January transfer window.
However, Parish believes Zaha will remain at Palace – who are currently third in the Championship – with Holloway looking to keep hold of his best players to maintain their promotion push.
“Right now we’re concentrating on trying to get out of this league and the best way of doing that is adding to what we’ve got, not losing players,” Parish told talkSPORT.
“I think he will be a Palace player until the summer. He has said himself that he really wants to help us get promoted. You can see on the pitch how hard he is trying to achieve that.
“I think he will be a Palace player until the summer and then we will look at it. Obviously, we will look at anything that anybody offers us because we will be mad not to.
“If we feel we can move the club forward from doing certain things, then we will. So, never say never. But right now we are focused on trying to keep everyone in the squad.”
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