Sam Allardyce told talkSPORT that Everton will not call him to discuss the vacant leadership position at Goodison Park.
The Toffees are on the hunt for a new boss after Carlo Ancelotti returned to Real Madrid earlier this week.
Allardyce managed Everton for six months in the 2017/18 season as he guided the club from 13th to eighth place.
However, part of the Goodison Park loyalists were not happy with the former England manager’s style of play.
Everton are looking to name a third permanent manager since Allardyce’s sacking, with Ancelotti leaving after leading the Toffees to tenth place in the Premier League.
But the 66-year-old is certain he is not up for the job.
Big Sam, who left West Brom after failing to preserve his Premier League status last season, told talkSPORT: “I can’t see Farhad’s phone call [Moshiri – Everton owner] for me.
“There was a certain element to Everton unfortunately that started to complain about my style as always as he lives with me.
“It’s like that big, big tent over my head. You try to bring in what the football club needs, and it’s the results first, and then you increase the results by buying better players and playing more attractive football.
“I don’t see them giving me a ring. They gave me a ring because they were desperate the last time!
“As a man who was able to get them out of a difficult position, which we did very, very quickly by the way, they didn’t let me go on from there.
“It was the disappointing thing, so I can’t see that happening.”
Allardyce insists the Toffees need to sign better players if they are to break into Europe next season.
He added: “With the sum of money Farhad [Moshiri] put in the club, they really deserve better. But how do they get there?
“Stability and a recruiting policy must be the way to go if they are to be successful and get into the top six and then into the top four.
“You have to look at the recruitment and the quality of the players. They had one of the best managers in Europe and they still haven’t succeeded. So it has to be recruitment. “