The Toffees are determined to land the Ivory Coast international before Thursday's transfer deadline, but Palace are demanding at least £100m for the winger.
And according to the Guardian, that valuation means the deal is in effect dead.
Zaha is reportedly disappointed with Palace's decision to turn down Everton's bid, with the winger having believed the club would accept "reasonable" offers for him last summer.
Zaha is now holding out for a move to a European club, with the transfer window on the continent remaining open until the end of August.
Everton take on Palace on the opening weekend of the Premier League season.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.