Zaha has recently returned from the Africa Cup of Nations having been on duty with the Ivory Coast.
Arsenal have chased the Crystal Palace winger for several weeks after it emerged the 26-year-old wanted to move to the Emirates.
Zaha is a boyhood fan and has made it clear he sees his future away from Selhurst Park.
He tweeted: “Source close to Wilfried Zaha says Everton want to sign him and talks to be held this week. Zaha preference is still for move to Arsenal”.
Zaha still favours a move to the Gunners despite Everton’s interest, but Palace’s £80m price tag is a big ask for a team whose transfer kitty is less than £50m.
The Eagles have already lost Aaron Wan-Bissaka to Manchester United for £50m.
They are therefore loathed to lose another of their prized assets and no longer requires the financial windfall.
Zaha has stated his desire to play Champions League football, something Palace are unable to offer.
Everton and Arsenal are in the same boat, but both have higher ambitions than the Eagles.
READ MORE: Arsenal fans demand Rob Holding be named captain.
The Toffees showed in glimpses last season that they could challenge the top six under the leadership of Marco Silva.
The Portuguese boss was afforded almost £100m during his first summer in charge at Goodison Park.
And 12 months on the club’s hierarchy are not holding back and are prepared to back Silva once again.
A £22m deal for Andre Gomes has already been finalised after he impressed while on loan from Barcelona.
Premier League winner Fabian Delph has also joined from Manchester City although it is looking increasingly likely that Idrissa Gueye will swap Merseyside for Paris.