Arsenal has been hot on the trail of the England international, but Parish has insisted the club will only sell the talented forward if the South London club receives an offer it can't refuse.
"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.
"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."