The club confirmed there had been an initial rejected bid, reported to be £52m, for the 26-year-old Ivorian.
On Monday it was claimed there was now a new offer of £55m plus midfielder James McCarthy and forward Cenk Tosun.
“A bid was made over the weekend which was turned down. Both clubs agreed that was the end of the matter,” Everton said in a statement.
Manager Marco Silva and director of football Marcel Brands have recruited midfielder Fabian Delph and goalkeeper Jonas Lossl this summer, and completed the permanent signing of last season’s loan player Andre Gomes.
They are set to lose midfielder Idrissa Gueye to Paris St-Germain, with the 29-year-old expected to complete his move to the French champions this week.