The 20-year old winger, who made his England debut recently, is being tracked by the likes of Manchester United and Arsenal but Parish has made it clear that the South London club are not yet prepared to offload the promising talent.
"He will definitely be playing at Crystal Palace after January," Parish told talkSPORT. "Why would we sell him? What would we achieve by selling him?
"We've been speaking this week with [Zaha's] representatives. Right now we're focused on getting out of this division.
"Nobody has contacted me from any of the clubs who are supposedly interested in him. We will have to cross that bridge when we come to it.
"I want all our players straining as hard as they possibly can to get us into the Premier League and for them to achieve all their ambitions with us, so it is not a deal I would particularly favour.
"But, if something was put in front of us and we spoke to the player and he wanted to go we would have to consider it. But right now we're just focused on keeping the squad together."