Duncan Ferguson will remain as Everton caretaker manager for Sunday's Premier League game at Manchester United.
The former Blues striker took temporary charge at Goodison Park last week following the sacking of Marco Silva.
He led Everton to a 3-1 home victory over Chelsea in his first game on Saturday.
The club are continuing to weigh up their options as regards a permanent manager - with ex-boss David Moyes still figuring heavily in discussions.
Shanghai SIPG coach Vitor Pereira withdrew his interest on Tuesday in favour of staying in China.
The Portuguese was under consideration but Everton had made no firm decision on whether to appoint him.
The Blues are expected to investigate the possibility of Carlo Ancelotti's availability after the 60-year-old Italian was sacked by Napoli despite guiding them to the Champions League knockout phase.
Everton also held informal talks with Unai Emery after he was sacked by Arsenal but that has gone no further at this stage, while Bournemouth's Eddie Howe has admirers in the Goodison Park boardroom.
Ferguson, who will be assisted again at the weekend by coaches John Ebbrell and Francis Jeffers and goalkeeper coach Alan Kelly, made an impressive impact in his opening fixture in charge.
The Blues came into the game against Chelsea having lost their previous three games, including a 5-2 thrashing in the Merseyside derby by Liverpool.
But a goal from Richarlison and two from Dominic Calvert-Lewin gave them a much-needed win to move them away from the relegation zone and up to 14th in the table.