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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.