Rafael Benitez is in prime position to be offered the Everton manager's job after a third round of talks with the club's hierarchy.
Everton are taking their time to appoint a successor to Carlo Ancelotti, who left to take over at Real Madrid.
Nuno Espirito Santo, who left Wolves at the end of last season, has also been considered and remains a candidate.
Former Liverpool, Chelsea and Newcastle manager Benitez, however, is now firm favourite.
He could become the first man to manage both Merseyside clubs, having won the Champions League and the FA Cup during a six-year spell at Anfield.
Everton are determined to cast their net wide for a manager before making a final choice.
Benitez's appointment would be contentious as many Everton fans were angered when he described them as a "small club" following a drawn Merseyside derby in February 2007.
The Spaniard, who still lives in the area, is understood to be keen on the challenge of reviving Everton and believes his methods would win over sceptical supporters.
He received a hostile reception from Chelsea fans when he was appointed their interim manager in November 2012 - the club's intense rivalry with Liverpool was in many supporters' minds - but ended up taking the Blues to third place in the Premier League and winning the Europa League.
Benitez last managed in the Premier League at Newcastle, where he was a hugely popular figure with fans, before moving to China for a spell at Dalian Professional.