Sky Sports News reported the 63-year-old would be informed at a meeting with majority shareholder Farhad Moshiri that his services are no longer required.
The writing has been on the wall for several months despite Allardyce’s public protestations to the contrary.
The former England manager has failed to win over a large section of the Everton fanbase despite lifting the club from 13th in the Premier League when he took over at the end of November to finish eighth.
Allardyce seemed to accept his fate after the Toffees’ final match of the season, a 3-1 defeat by West Ham, on Sunday.
He said: “Contract for next year. Confident? I can’t quite say confident after all the rumours I’m reading in the paper. Generally there’s no smoke without fire. We’ll wait and see when we meet up.”
A dismal start to the season under Ronald Koeman had Everton fearing being sucked into a relegation battle but stability and a push towards the Europa League spots did not placate the Everton support after Allardyce was given an 18-month contract.
Former Watford manager Marco Silva is the favourite to take over and could complete the move to Goodison Park six months after the club failed to prise him away from Vicarage Road.
The Hornets refused to let Silva go only to sack him in January, citing the disruption caused by Everton’s “unwarranted approach” for a major dip in form.
Shakhtar Donetsk coach Paulo Fonseca has also been linked with Everton as well as West Ham, while Louis van Gaal, Andre Villas-Boas, Sean Dyche, and Eddie Howe are other names reportedly in the frame.
Allardyce isn’t the only man set for the Goodison exit.
Robert Elstone has left his role as Everton chief executive to take on the top job in rugby league. Elstone, 54, leaves after 13 years to become the Betfred Super League’s new chief executive, filling the role created by the departure of Roger Draper in January.
Meanwhile Southampton chairman Ralph Krueger believes Mark Hughes has proven the “perfect” fit, with negotiations well under way to extend the manager’s St Mary’s stay beyond the summer.
Hughes was brought in to stave off relegation in March after floundering Mauricio Pellegrino was fired, managing just that as Southampton finished in 17th spot.
The Welshman only penned a short-term deal but chairman Krueger has been impressed by his work and talks to keep him are going on.
“The decision to go with Mark in the time frame that we had to meet him and to bring him in was very tight, but everything since they’ve been here has been natural and the fit has been perfect,” he said.
Krueger admitted the club had underappreciated the “negative storm” they were in until early February.
“We’ve gone a completely different direction when you look at him (compared to four successive foreign managers),” he said.
“But it just feels like the right hire at the right time for the club, and also I feel it was the right fit for them and with their experience, too.”
“So, we’re in really good conversation. We began these conversations last week and they continue here, and we will build on them.
“That’s all I can say to that right now, but we are in good conversation.”
It appears a case of when rather than if Hughes signs a new deal at a club who have pledged to learn from this season’s mistakes.
Pre-season will take the club to China — home of the Gao family, who became owners last August — and Krueger knows a balance is needed between keeping the best players and not allowing unhappy individuals to throw off the dressing room.
Last summer Saints dug in their heels to keep Virgil van Dijk but the wantaway defender, like so many before him, moved to Liverpool in January.
Krueger concedes there was an issue with “the dressing room that we created through some of decision-making over the last years”, which was down to club strategy as well as player recruitment and management.
“We want to have a dressing room of players who want to be here,” Krueger said. “That’s the most important thing.”
“We put (Pellegrino) in a pretty tough space and we take responsibility for that.
“But we needed to make that stand and I think it was an important stand to take and we’ll learn and grow from that.
“But I think we also have to get back to the Southampton way of having a locker room full of players that want to be here, whatever that ambition is.
“And if somebody ends up being in a Champions League final like Sadio Mane, we should be proud of that and should see it as an accomplishment.
“And I think that’s something we’ll get back to.”
Elsewhere Brighton boss Chris Hughton has been rewarded with a new contract after keeping the Seagulls in the Premier League.
The 59-year-old former Ireland international and former assistant manager to Brian Kerr with the national team has agreed fresh terms until 2021 after guiding Brighton to 15th place this season.