Everton remain interested in bringing Marco Silva to Goodison Park as Allardyce's replacement, but despite being now unemployed, appointing him as their manager still faces some challenges.
Allardyce replaced Ronald Koeman after a disastrous start to the season, but he was not first choice as they failed with an approach for then Watford boss Marco Silva.
Sam Allardyce and David Moyes are both set to depart the clubs which they helped retain Premier League status this season.
Former Watford boss Marco Silva and and Shakhtar Donetsk boss Paulo Fonseca are the bookies favourites to replace Allardyce, wither veteran Dutch tactician Louis van Gaal also listed as a contender after his spell at Manchester United ended in May 2016.
According to The Mirror, the Toffees hierarchy and Allardyce will hold a meeting within the next 48 hours and the 63-year-old is expected to be told that his contract will be terminated a year early.
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.
Speaking on Sky Sports last night, Allardyce said: "Who knows what is going to happen next?"
Sam Allardyce believes that he was wrongfully dismissed.
Moshiri is now expected to reach a settlement on the final year of Allardyce's deal before moving quickly to appoint his successor.
'It is as much as Wayne, his representatives and the board of administrators and what they do, which is the place it's in the intervening time, ' Allardyce mentioned.
On Tuesday morning, The Mirror put out a story saying things could get more complicated for Everton, since there's another club in the race for Silva.
"The season has finished, I'm going to have a meeting with (owner) Farhad (Moshiri) this week and then I'm going on my holidays".