Marcelo Bielsa has arrived in London for further talks with the Everton hierarchy as they search for a successor to Frank Lampard.
The 67-year-old former Leeds United manager is a top choice for Everton owner Farhad Moshiri.
Sean Dyche, who has been out of work since being sacked by Burnley in April, is the other main candidate to take over at Goodison Park.
The Toffees hope to have someone in place by the weekend.
Bielsa is believed to have reservations about Everton’s squad composition and ability to play their high-paced style of football, as well as taking over mid-season.
But the fact that he flew to England to further discuss the possibility shows there is still interest from both sides.
Dyche is also in the final round of talks.
If Everton put someone in place before the weekend, they would have a week to work with the players before welcoming Premier League leaders Arsenal next Saturday.
Everton sacked Lampard after Saturday’s 2-0 defeat at West Ham left them 19th in the table with just three wins and 15 points from 20 games.
