Burnley manager Sean Dyche is the favourite to succeed Ronald Koeman at Everton.
Koeman was today sacked at Goodison Park after a poor run of results.
And bookmakers have installed Dyche as the favourite to take over at the Premier League club.
Seventh-placed Newcastle United take on Burnley at Turf Moor on Monday, October 30.
United manager Rafa Benitez was also linked with the post before Koeman lost his job.
Everton are third-bottom in the Premier League after winning just two of their opening nine league games.
A statement from the club read: "Chairman Bill Kenwright, the board of directors and major shareholder Farhad Moshiri would all like to express their gratitude to Ronald for the service he has given to the club over the past 16 months and for guiding the club to seventh place in last season's Premier League campaign."
Koeman led the club to a seventh-placed finish last season, his only full campaign at the helm after arriving from Southampton, but has had a torrid time of late.
Two home defeats in four days, 2-1 to Lyon in the Europa League and 5-2 against Arsenal on Sunday, and the chorus of boos that followed each time proved the end of the line for 54-year-old.
The departure of Romelu Lukaku, who joined Manchester United for £75million in the summer, left the Toffees light up front but Everton's use of those funds has been questioned.
Gylfi Sigurdsson and Davy Klaassen cost almost £70m between them and Wayne Rooney was brought back from Old Trafford on a high-profile free transfer, but Lukaku was never adequately replaced.
A further £55m was spent on Sunderland goalkeeper Jordan Pickford and defender Michael Keane, yet the Toffees have conceded 18 goals in nine league games, and only rock-bottom Crystal Palace have a worse goal difference.
Koeman reported for training at the club's Finch Farm facility on Monday morning, with preparations for Wednesday's Carabao Cup game at Chelsea seemingly under way.
But Kenwright and chief executive Robert Elstone were later reported arriving on site unexpectedly and Koeman's dismissal was confirmed soon after.
Koeman becomes the third top-flight boss this season to lose their job, following Frank de Boer at Palace and Craig Shakespeare at Leicester City.
Speaking after his final outing in the dugout, Koeman confronted speculation over his position head-on.
''I still believe I can change the whole situation, but everybody knows how it works in football," he said. "That's all I answer about this situation.
''If you start to think negatively, then maybe there is no solution. I'm not like that. All the rumours in the newspapers are normal.
"All these kinds of decisions are not in my hands.''