The Cottagers have been dragged towards the relegation zone with just one win in six, but are still considered outsiders for the drop at 14/1.
Paul Lambert is the 9/4 second favourite in the 'next Premier League boss to leave' betting after Aston Villa were made odds-on for relegation with another defeat at the weekend.
Sky Bet Football Trader Chris Spicer said: "It comes as somewhat of a surprise that Jol has been backed this morning but Fulham's form of late has been far from impressive, failing to beat strugglers Wigan, Southampton and QPR in recent weeks."
Meanwhile, Sky Bet have opened betting on whether Vincent Kompany's red card appeal will be successful, going 11/4 for it to be overturned by the FA.
 
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