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Bookmakers William Hill reckon the Portuguese coach an 8/11 bet, with Southampton's Mark Hughes and Cardiff City's Neil Warnock the second-favourites to part ways with their employers at 7/1.
Goals from Chris Wood and teenager Dwight McNeil gave struggling Burnley a much-needed 2-0 Premier League win over West Ham United at Turf Moor on Sunday.
The re-born Paul Pogba scored twice, for the second time since Jose Mourinho's departure from the club, as Manchester United beat Bournemouth 4-1.
Chelsea's win moved them temporarily into third on 34 points, ahead of Arsenal on goal difference.
Manchester City stumbled to the Premier League's shock defeat of the season so far with a sensational 3-2 reverse against Crystal Palace.
Manchester City bounced back from two consecutive defeats to beat Southampton 3-1 on Sunday.
Chelsea kept up their pursuit of the Premier League's top three clubs with a 1-0 win away to London rivals Crystal Palace on Sunday.
Liverpool's goals came from Georginio Wijnaldum - his first away from home in the Premier League.
Everton had created most of the early chances as they looked for their first victory at Arsenal since January 1996.
Needing a two-goal win to depose Liverpool at the top of the table, Chelsea struggled to make clear chances.
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