Beaten 4-0 by Manchester United on Sunday, the Toffees find themselves in the bottom three after five games.
Despite spending heavily in the summer, the Merseysiders have picked up just four points, scoring two goals and conceding 10 in the process.
Things haven’t gone well in Europe either, with Everton losing 3-0 to Atalanta last week.
And their Dutch boss has been backed into favouritism in the Sack Race market despite being as long as 8/1 before a ball was kicked this weekend.
Meanwhile, Manchester City and Man United are locked at the top of the table level on points.
Alex Apati of Ladbrokes said: “We’ve already had one managerial casualty this season, and Koeman could soon become the second if this horrible run continues.”
Ladbrokes Latest Betting:
Next Premier League Manager to Leave
Ronald Koeman – 15/8
Slaven Bilic – 2/1
Eddie Howe – 10/1
Craig Shakespeare – 12/1
Rafa Benitez – 12/1
To win the Premier League – 300/1
To finish in the Top Four – 25/1
To go down – 66/1
Premier League Outright Winner
Man City – Evens
Man United – 13/5
Chelsea – 5/1
Tottenham – 16/1
Arsenal – 25/1
Liverpool – 25/1
Click here for all our Premier League odds.
All Odds and Markets are correct as of the date of publishing