The Toffees want to have a new man at the helm as soon as possible ahead of the closure of the transfer window, with fresh faces still eyed at Goodison Park.
They have zeroed in on three options in the shape of ex-Fenerbahce coach Vitor Pereira, former Chelsea boss Frank Lampard and current caretaker Duncan Ferguson.
All three candidates will hold a final round of talks with Everton on Friday before the club’s owner Farhad Moshiri makes the final decision.
Pereira was expected to be handed the job, but a fan backlash against the Portuguese taking over appears to have thrown the race open.
Lampard has been out of work since being sacked by Chelsea and is relishing the chance to jump back into management with Everton.
Ferguson stepped in when Rafael Benitez was sacked and some fans believe he could be the best choice.
Everton are only four points above the drop zone in the Premier League following a poor run of form.