Arsenal have been the England international's main admirers and had begun neghotiations with the Eagles, in the hope of securing a £12 million deal this month.
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However, Parish has insisted they will only sell talented forward if the south London club receive an offer they can't refuse.
He told talkSPORT: "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.
"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."