The Hoops chief has been linked with a job with the Premier League side.
Despite relegation with Newcastle, Moussa Sissoko is heading to Euro 2016.
The Greek international has never made an impact at Craven Cottage.
The talented defender came on against St Johnstone.
Everton will also treble the Southampton manager's wages to tempt him into the switch.
The Owls meet Brighton at Hillsborough in the first leg on Friday.
The Uruguayan was heavily linked with the Forest job.
Karl Robinson would build his side around Lewis Cook, if appointed.
Paul Merson believes Newcastle and Tottenham will draw on Sunday.
Everton parted company with Roberto Martinez on Thursday afternoon.
With the road now clear for the remaining “short campaign” to the EU referendum, both sides are accusing their rival of panic: David Cameron for allegedly warning of future European wars, Iain Duncan Smith and Boris Johnson for assorted wild exaggerations.
Stephy Mavididi netted twice for Arsenal's under-21 side as they beat Aston Villa.
Newcastle are reportedly preparing for Everton to make a move for Rafael Benitez.