Everton owner Farhad Moshiri has held talks with Marcelo Bielsa about taking charge at Goodison Park.
The Daily Mail says Bielsa is Everton's top choice to save them from relegation after Frank Lampard was sacked as manager on Monday.
Lampard was relieved of his duties at 3pm on Monday after 357 days in charge. He leaves Everton 19th in the Premier League having made their worst ever start to a season, with 15 points from 20 league games.
Bielsa, who left Leeds last season having worked wonders to re-establish them as a Premier League club, has held talks with Everton's owner Moshiri and wants to know about their transfer strategy a week before the window closes.
Everton officials know what is riding on this appointment and they believe that appointing a manager with Bielsa's reputation and his high-energy, attacking style could galvanise them with half the season still to play.