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Everton head into the game 16th in the Premier League and without a win in their last four games in all competitions.
“It’s crucial – I made good contact with the board of the club, but everybody knows I’m not stupid,” Koeman told Sky Sports.
“Finally you need wins and you need points. Maybe an ugly win is the best for this Sunday.
“I have really good contact with the board but if there is unhappiness around the club, and if the team is not winning, finally the manager will always pay the bill and that’s football and I accept that.
“We had eight or nine new players and that makes it even more difficult. Everybody knows that new players need time to adapt to the Premier League, to the competitions.”
Koeman can be backed at 11/4 to be the next manager to leave his job in the Premier League and those odds will be slashed if Everton come up short against Arsenal.
Everton have won two and drawn one of their last four league home games against the Gunners and are on offer at 3/1 to add another win on Sunday. Arsenal are priced at 10/11, with the draw available at 27/10.
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