Marcelo Bielsa has arrived in London for further talks with Everton's hierarchy as they search for a successor to Frank Lampard.
Sean Dyche, who has been out of work since being dismissed by Burnley in April, is the other main contender to take over at Goodison Park.
The Toffees hope to have someone in place by the weekend.
Bielsa is believed to have reservations about the composition of Everton's squad and its ability to play his trademark high-tempo style of football, as well as taking over in mid-season.
But the fact that he has flown to England to discuss the possibility further shows there is still interest on both sides.