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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.