Carlo Ancelotti has arrived on Merseyside this afternoon for talks with Everton about becoming the new manager at Goodison Park, Sky Sports News understands.
Ancelotti, who was relieved of his duties as Napoli manager and replaced by Gennaro Gattuso last week, has been a target for Everton's majority shareholder Farhad Moshiri and chairman Bill Kenwright since Silva's departure.
The 60-year-old won the Premier League, the FA Cup and the Community Shield during his tenure at Chelsea from 2009 until 2011, and has lifted three Champions League trophies over the course of his managerial career.
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Sky Sports News understands Ancelotti is Everton's No 1 choice to become their new manager and current interim boss Duncan Ferguson would remain as part of the first-team coaching staff, should the Italian be appointed.
The Scot, who scored 65 goals in 253 matches for Everton during two spells with the club as a player, has overseen a 3-1 win over Chelsea and a 1-1 draw away at Manchester United.
He will remain in charge for their Carabao Cup clash with Leicester on Wednesday.
Other candidates on the Everton shortlist include David Moyes, who has his admirers in the Everton boardroom and is believed to have met with the club, though his appointment would be more a short to mid-term decision.
Manchester City assistant manager Mikel Arteta is also among those who have been linked with the role, although the Spaniard met with Arsenal officials in the early hours of Monday morning to begin talks about becoming Unai Emery's replacement at the Emirates Stadium.
Kevin Campbell: Ancelotti can bring about blue revolution on Merseyside
Former Everton striker Campbell told Sky Sports News: "It is about time Everton really put the shackles off and actually got a manager who is a perennial winner.
"The guys who they have had before have been winners but they haven't been of the calibre of an Ancelotti.
"If Ancelotti goes in at Goodison then I would love to see Duncan Ferguson on his staff. He has proven to be really good for the football club right now.
"Moving forward a man like Ancelotti knows exactly what to do. He knows how to set teams up and he knows how to win.
"Get him in and back this guy and then hopefully there could be another revolution - a blue revolution on Merseyside."