Palace are not interested in a deal whereby Manchester United would buy Zaha next month and then loan him back to the Championship club for the rest of the season.
Parish dismissed the notion saying: "That idea doesn't strike me with joy. I'm not sure what you would get out of a player.
"We just want to put a lid on it now. All I care about is getting promoted. In the end, that's all I care about.
"Wilfried is on a four-and-a-half year contract and every real offer that comes in, we look at it in the context of what's best for our chances of getting promoted.
"Every decision we make, will it help us get promoted? Yes or no? If it's a yes, we'll do it, but if it's a no, we're not going to do it, so that's the test of everything at the moment.
"We want stability and all of our best players available and try to get promoted - that's our goal. Everybody else will have to fit in around that."