Marcelo Bielsa has arrived in London for further discussions with Everton’s hierarchy as they seek a replacement for Frank Lampard.
Everton owner Farhad Moshiri prefers the 67-year-old former Leeds United manager.
Sean Dyche, who has been out of work since being fired by Burnley in April, is the other main contender for the Goodison Park job.
By the weekend, the Toffees hope to have someone in place.
Everton is not for sale, according to Moshiri.
Who could be the next manager of Everton?
Bielsa is said to be concerned about the composition of Everton’s squad and its ability to play his trademark high-tempo style of football, as well as the fact that he is taking over in the middle of the season.
However, the fact that he has flown to England to further discuss the possibility shows that there is still interest on both sides.
Dyche is also in the final round of talks.
If Everton can find a replacement before the weekend, they will have a week to work with the players before hosting Premier League leaders Arsenal next Saturday.
Everton sacked Lampard after their 2-0 loss to West Ham on Saturday, which dropped them to 19th in the table with only three wins and 15 points from 20 games.
Lampard is ‘disappointed’ that he was unable to achieve more at Everton.
Lampard succeeded Rafael Benitez on 31 January last year, when the Spaniard was sacked with the Toffees in 16th place, four points above the relegation zone.