Sky Sports revealed on Wednesday that Premier League table-toppers Manchester United have expressed an interest in acquiring the highly-rated forward.
A January approach is said to be on the cards, with the Red Devils eager to add another player of considerable potential to their ranks.
Palace are aware of the reports, and the incessant rounds of speculation regarding their talented 20-year-old, but Parish insists they will only sell if big money is put on the table.
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."