Goal.com report that a defeat this weekend to Leeds in the FA Cup could be enough to see the Italian dismissed before the end of the season.
Mancini has struggled this season after leading City to the title last time around.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.