This season marked the first time that a club managed by Allardyce were relegated from the Premier League as his West Bromwich Albion side were only able to finish 19th in the Premier League.
He is now available once again after choosing to step down as boss at the Hawthorns.
Everton are now looking for a new manager following the shock exit of Carlo Ancelotti to Real Madrid, but Allardyce does not feel he will be going back to Goodison Park.
Allardyce steadied the ship at Everton and guided them to an eighth placed finish in the Premier League.
He feels that given the Toffees did not give him the chance to kick on last time there is little chance they will pick up the phone to him again.
“There was a certain element in Everton unfortunately that started to complain about my style as always, it lives with me, it’s like that great big ten tonne weight on top of my head”, Allardyce said on talkSPORT.
“You try and bring to the football club what is needed and that’s results first and then you add to results by buying better players and creating and being more attractive in terms of the football that you play.
“I can’t see them giving me a ring.
“They gave me a ring because they were desperate last time and as a man that’s capable of getting them out of a difficult position, which is what we did, very, very quickly by the way.
“They didn’t let me go on from there, that was the disappointing thing, so I can’t see that [a return to Everton] happening.”
It remains to be seen who will take over the managerial post at Everton, but the club are holding talks with former Wolves boss Nuno.
