Caretaker boss David Unsworth has stressed Everton's next permanent manager will need "time, patience, support and backing".
It seems the Toffees will soon have a new man in charge, with Unsworth today saying "talks are ongoing" between the club and "a few people".
It is understood that includes discussions with representatives of former England boss Sam Allardyce, who had publicly ruled himself out of the running just under two weeks ago.
Shakhtar Donetsk coach Paulo Fonseca is also a candidate, according to reports, while Republic of Ireland boss Martin O'Neill's name has been mentioned as well.
Unsworth, who stepped up from the Under-23s following Ronald Koeman's sacking on October 23, said he would still be in charge for tomorrow's clash with West Ham as far as he was aware.
Asked for his understanding of the managerial situation, he said: "As we sit here right now, I believe the board are talking to a few people.
"Talks are ongoing, but nothing has been finalised yet with anybody. So I continue to do what I was asked to do five weeks ago."
Asked directly about Allardyce, Unsworth said: "Sam is a top manager, but I think it would be wrong of me to talk about individuals.
"I have seen the names that have been bandied about - all top managers. Whether there's truth in the names of some, or all, or none, I don't know.
"But whoever gets the honour of being Everton manager will have my full support and my full backing."
Everton have won only one of the seven games of Unsworth's temporary spell to date and lost five of them, with their last two outings a 5-1 home loss to Atalanta and 4-1 reverse at Southampton.
Unsworth added: "I think we need our best players fit, quickly, some proven Premier League recruitment in early January and I think we need to win a couple of games and get confidence flying again.
"When confidence is low, it takes a bit of time to build that back up. I don't think there's a quick fix - I think whoever gets the job needs time, patience, support and backing."
Unsworth has expressed his desire to have the permanent job, but the way his temporary stint has panned out has left him looking entirely out of the frame.
Everton go into Wednesday's league contest at Goodison Park having finished Sunday's at Southampton 16th in the table, two points better off than 18th-placed West Ham, who are managed by ex-Toffees boss David Moyes.
Appointing Allardyce would see Everton bring in a man who steered Sunderland and then Crystal Palace away from the trouble in the past two seasons.
He had said on November 15 that rather than wait for Everton to reach a decision, he would "move on to something else".
It was in that week that it emerged Everton had had overtures for Watford boss Marco Silva rejected, and nothing materialised from Burnley manager Sean Dyche being linked with the vacancy.
Dyche said today as he admitted he would be pleased to stop getting asked about the Everton job.
"Sam is a terrific character. His record speaks for itself, with that he's done in various different guises at different clubs," Dyche said.