We understand Allardyce will be summoned to a meeting within the next two days to be given the news his contract, that has a year to run, will be terminated.
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.
This will be music to the ears of Everton supporters who for one reason or another do not believe the one-time England boss is good enough for them.
According to reports, Allardyce will receive a £6 million pay-off from the Premier League club.
Allardyce is just six months into the 18-month deal he signed in November, after he clawed Everton back from serious decline and relegation nightmares to an eighth-place league finish.
Ireland trouble Pakistan on Test debut
The 33-year-old started excellently with the ball as Pakistan's openers were put through a testing period. The seventh-ranked Test side in the world fought back through Haris Sohail's 31 and Asad Shafiq's 68.
"It's my job to turn that around", he told Sky Sports.
The 63-year-old is set to hold talks with Everton owner Farhad Moshiri.
Allardyce's backroom staff of Sammy Lee, Craig Shakespeare and Martyn Martgetson are also set to depart. Current Shakhtar Donetsk manager Paulo Fonseca is the favourite to replace Moyes.
Chants demanding Allardyce's dismissal have grown in ferocity for weeks, creating an undignified spectacle at Everton's games. A statement from the club at the time blamed an "unwarranted approach by a Premier League rival" for Silva as being the catalyst for the destabilisation of his tenure.
"Go and see what he (Allardyce) was doing when he was 40 years old, or see what he was doing in his first seven seasons as a coach".