Palace are said to value Zaha at £75million but Parish has suggested there would be no point making a move at this late stage.
He said: ”It would be a ridiculous point to do it, wouldn't it?
“I mean to go the whole transfer window and only think about it now to come in with a bid would be ridiculous."
Palace boss Roy Hodgson revealed he spoke with Zaha last week and received no indication that the Ivorian wanted to leave.
Chelsea transfer news: Could Wilfried Zaha leave Crystal Palace? (Image: GETTY)
Chelsea transfer news: Steve Parish has given an update on Wilfried Zaha (Image: GETTY)
It would be a ridiculous point to do it, wouldn't it?
Crystal Palace owner Steve Parish
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"No, nothing at all on [the rumours],” he said.
“I don't read those stories to be perfectly honest, they circulate all the time.
"I spoke to Wilf yesterday and he certainly gave me no indication it was true about wanting to quit the club.
"In fact, we were talking about how good the new signings were and how they would help us.