Parish says he understands the 28-year-old's position and is confident that Zaha's performances will never drop in a Palace shirt, regardless of his future.
"We understand his position," Parish told BBC Sport. "It's no secret that he would like to challenge himself. But it has to be right for the football club. He understands that as well.
"If those two things collide then we will have to look at it. But right now, we are two days into the transfer window so it's a bit early to talk about it.
"(He) continues to be an incredible talisman for the team. Obviously, there is lots of talk about transfers and all that kind of thing.
"All I know is that when he crosses the white line for Crystal Palace he gives 100 per cent. Everything else, what will be will be. There's a lot of love around the club for Wilfried and everything he has done for us as a football club."