Everton owner Farhad Moshiri will hold a final round of talks on Friday before deciding on a managerial successor to sacked Rafael Benitez.
Moshiri pulled back from appointing favoured choice Vitor Pereira - who remains a serious contender - after an angry reaction from supporters.
That left Frank Lampard to re-emerge as a serious candidate following an initial round of talks.
Caretaker manager Duncan Ferguson is the other name on Moshiri's list.
Pereira was in pole position after impressing Moshiri in his interview, but a toxic reaction from Everton fans to the 53-year-old's proposed appointment appeared to lead to a pause, although he remains very much in Moshiri's thinking.
In a limited field Lampard, who finished fourth and reached the FA Cup final in his one full season at Chelsea before being sacked in January 2021, appears the choice who would at least unite an increasingly disgruntled fanbase, but he must also await Moshiri's final decision.
Pereira tried to placate fans by conducting a lengthy television interview detailing his talks with Everton's powerbrokers and his plans should he be appointed, but it has failed to erase concerns about his credentials from supporters. He is currently out of work having been sacked by Turkish club Fenerbahce in December.
Everton's attempts to find a successor to Benitez have appeared dysfunctional from the moment an ill-fated attempt to appoint Belgium coach and former manager Roberto Martinez - the first of five Goodison bosses sacked by Moshiri in May 2016 after fan protests - was blocked by the country's Football Association, who would not sanction such a move in a World Cup year.
There was a sit-in and protests after Saturday's home defeat by Aston Villa. They have continued this week outside the club's city centre headquarters and also at Goodison Park on Wednesday night, when hundreds of fans gathered at the stadium.
Moshiri's regime and chairman Bill Kenwright were targets for angry supporters, but there was also fury and banners directed at agent Kia Joorabchian, who has been identified by Everton fans as wielding too much influence over the owner.
Amid the unrest, Everton have slumped towards the relegation zone after one win in 14 league games, only four points off the bottom three.
Meanwhile, the Toffees have confirmed midfielders Abdoulaye Doucoure and Fabian Delph will be out for a minimum of four weeks.
Doucoure was forced off with a groin injury against Aston Villa last weekend, while Delph picked up a thigh problem in training.