If true, the latest developments mark the beginning of a series of significant changes at Goodison Park this summer that may include a new director of football in the form of Marcel Brands, the departure of the club's highest earner in Wayne Rooney, and a new chief executive.
The 63-year-old is due to meet Everton majority shareholder Farhad Moshiri for talks this week, and sources said both parties are expected to agree to a parting of ways.
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However, it looks like there will be an update this week, with Allardyce adding on Sky Sports' Season Review - Managers Special: "It's moved on with his representative and the board from here, which I believe may be Wednesday".
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Allardyce secured an eighth-place finish for Everton in the Premier League after just two defeats in their final nine league matches. With a year left on his contract, Allardyce can expected a handsome payout to ease the parting blow.
Two months later, after a downturn in results, Silva was sacked by Watford, who released a statement saying that an "unwarranted approach by a Premier League rival" had effectively destabilised the 40-year-old and, as a outcome, their season.
"They'll still continue to make it up that we've had a row, and that he's walked out on me, or that I've had a row with him and all that".
"They have always been a club that get behind their players and their manager."
"The season is finished and I am going to have a meeting with Farhad [Moshiri, the club's leading shareholder] this week and then I will go on my holidays".