Corriere dello Sport report that the two clubs are tracking the Brazilian centre back, who has impressed this season.
Marquinhos signed for Roma only last year, but they could be forced to sell if a big offer comes in.
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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.