Everton joined Arsenal in pursuing a deal for the 26-year-old over the weekend but their opening bid of £52m was turned down by the Selhurst Park outfit, who value Zaha closer to the £80m mark.
Reports making rounds on Monday suggested that Everton had returned with an improved offer of £55m and were also including midfielder James McCarthy and striker Cenk Tosun in the deal.
With Arsenal turning their attention to Lille winger Nicolas Pepe, it was thought that Everton would have a leeway to get the deal over the line but they have issued a statement confirming an end to discussions.
"Everton categorically denies a bid has been submitted to Crystal Palace for Wilfried Zaha that included an increased sum plus Cenk Tosun and James McCarthy," the Toffees revealed in a statement to Sky Sports.
"Everton and Crystal Palace have very good relationship.
"A bid was made over weekend which was turned down. Both clubs agreed that was end of matter."
Zaha, who made two international appearances for England in non-competitive games before switching allegiance to the Ivory Coast, featured 34 times in the Premier League last season and scored 10 goals.
Everton have been busy in the transfer market, getting deals for Andre Gomes, Jonas Lossl and Fabian Delph done, while Ademola Lookman and Idrissa Gana Gueye have departed for RB Leipzig and Paris Saint Germain respectively.
