The Spanish media outlet claim club president Florentino Perez wants more defensive options and has identified the Brazilian as the perfect target.
'Los Blancos' captain Sergio Ramos has not had the best start to the season, while Raphael Varane is considered too much of a risk due to injury issues.
Real's other options, Nacho and Jesus Vallejo, are deemed too inexperienced to take on a starting role in Zinedine Zidane's starting XI.
Therefore, Perez is willing to pay €80m (£71m) to secure Marquinhos' services, and could sanction a January move for the defender.