The Mirror says owner Farhad Moshiri held a series of meetings through the afternoon with key Goodison boardroom figures, including director of football Marcel Brands.
That saw the billionaire majority shareholder make initial contact with Nuno Espirito Santo, the former Wolves manager, to sound out the Portugese coach about the club's vacant position.
Nuno is available after being shown the door at Wolves at the end of the season, and has already held talks with Crystal Palace and two clubs in his home country.
Moshiri is an admirer, but elsewhere at Everton there is more caution over a manager who lost the backing of the board at Molineux over his cautious, dogmatic style.
Brands wants to be certain the club gets the right character for the role, after the turmoil of five different managers in five years, and the shock of Ancelotti's untimely and disruptive departure.
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