Pellegrino is currently in charge of Malaga, where he has impressed after good spells in charge at Real Madrid and Villarreal.
He could face competition from Jose Mourinho, according to the Daily Mail, who report that Chelsea are looking at their various options with the season drawing towards a close.
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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.