Benitez was shown the door at Goodison Park on Sunday after a poor run of results led to fans demanding his head and worries over a potential relegation battle in the Premier League.
The Spaniard was hamstrung by financial fair play rules in the summer transfer window and was then given just two weeks of the winter window before the axe fell.
Everton are now looking at who should come next after Benitez and they have identified two leading candidates for the post.
It is claimed that Belgium coach Roberto Martinez and Benitez’s assistant at Everton, Duncan Ferguson, are those most keenly under consideration.
The Toffees may look to move quickly given the new manager through the door is likely to want to make signings in what time is remaining in the January window.
Ferguson could slot in as the new boss, however Martinez is currently employed as Belgium coach.
Belgium have qualified for the 2022 World Cup in Qatar and the jury is out on whether Martinez would be prepared to leave before the finals.
