The news means that David Moyes has returned into the odds-on favourite with Sky Bet for a return to Goodison Park.
Duncan Ferguson, who started his interim period as manager with a 3-1 victory over Chelsea on Saturday, is now at 6/1.
Unai Emery, recently sacked by Arsenal, has been linked with the vacancy and is fancied as an outside chance to become the next permanent boss.
Reports say that the Toffees held an 'informal meeting' with Emery this week although he wants more time to think about his next move.
Rafa Benitez, former Bayern Munich manager Niko Kovac and River Plate boss Marcelo Gallardo are also in the market.
Odds correct at 1715 GMT (10/12/19)