Everton are set to take on Chelsea in League Cup in midweek.
Koeman has come under serious pressure after the Toffees’ disastrous start to their league campaign.
Everton are currently in the Premier League’s relegation zone, after losing 5-2 against Arsenal in front of their own supporters at the weekend.
Everton were abject during the contest, as they have been for much of the campaign so far.
And Barton believes that Koeman will be sacked this week, if Everton lose to Chelsea in the League Cup.
“Watching the highlights back, it could have been a lot more. You think how many saves Pickford made! It’s just a monumental collapse, it looks like,” Barton said.
“They have Chelsea away during the week, and I’d be surprised if he can go to Stamford Bridge and win. If they lose there, I think that could be the end of the manager. It looks like a managerial change is the only way out.”
Koeman was handed a great deal of money to spend at Everton, but their squad appears to have got worse over the summer.
The Toffees have struggled in an attacking sense, but they have also looked very shaky at the back.
Everton went into the campaign with the aim of breaking into the top six, but those hopes have already been extinguished.
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