As exclusively revealed by Goal.com, both Liverpool and Manchester City are weighing up bids for the youngster with Arsenal also tracking the teenager.
However, Parish suggested Palace will not be letting Zaha go on the cheap, saying that it would take a monumental bid to even get the club to begin negotiating a transfer.
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"[Zaha] is an extraordinary talent," he told the South London Press. "I said at the start of the season that keeping hold of Wilf would be like spending a lot of money on a transfer.
"Other sides can fly their kites but it would take £20 million before we even got interested.
"He has got the lot, provided he keeps his feet on the ground and continues working so hard on his game - then it will all come."
Zaha has impressed this season with some glittering performances including doubles in consecutive games against Wolves and Burnley.
And Parish explained the club's stance in terms of their ambitions to reach the top flight, insisting Zaha is central to their plans for promotion to the Premier League - and losing the youngster would be a huge blow.
He added: "People would have to compensate us accordingly for losing [Zaha's] talent - that is what a transfer fee is.
"All the teams have got to understand that you get £60m in TV money if you get into the Premier League, which is where we want to get. So we'd need to be compensated for reducing our chances of getting there."