The Bianconeri have endured a poor campaign and risk finishing outside of the European qualifying positions when the season concludes this weekend.
Former midfielder Antonio Conte is in the running to replace del Neri.
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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.