However the Toffees have also seen a bid turned down with Palace demanding around £80m.
And Zaha posted a cryptic message on Twitter with a picture of himself at the cinema with the caption suggesting he was turning his phone off amid the noise around his future.
He was wearing a t shirt that said: “Instagram flexing kills.”
Zaha now looks set to stay at Palace this summer despite pushing for a move to Arsenal with his brother publicly claiming he wanted to go.
Judicael Zaha said at the start of July: “Wilfried will always hold Crystal Palace and their fans in the highest regard and all the support they have given means the world to him.
“It is my brother’s dream, though, to play for Arsenal.
“Given all that Wilfried has given to Crystal Palace to help them remain a Premier League club, I hope Palace will be able to see their way to agreeing a deal with Arsenal that allows Wilfried to realise his dream of playing European football for the club he has supported since childhood.”
Arsenal were leading the race for Zaha but were unable to agree a fee with Palace and have now turned to Pepe who will join from Lille.
Arsenal have managed to agree terms on a £72m transfer with structured payments and the winger will make his decision on a deal today.
Sky Sports reporter David Reed said: “Pepe is due back from his holiday today after competing at the Africa Cup of Nations and Lille then expect him to make a decision on his future.