Mundo Deportivo reports that president Florentino Perez has taken advantage of the Italian giants' interest in signing Mateo Kovacic to sound out if the Serie A side would be open to negotiate the departure of the Argentina international.
Real Madrid have been heavily linked with Monaco starlet Kylian Mbappe this summer amid suggestions that Gareth Bale could be shown the exit door before the end of the transfer window.
However, it has been reported that Los Blancos are having second thoughts over the France international due to Monaco's high financial demands.
Therefore, reports claim that Real are considering making a move for Dybala as the youngster could represent a more affordable option.
Club chief Perez recently used Juventus' own enquiry over Kovacic to sound out whether the Champions League runners-up would agree to part ways with Dybala if Real make an offer worth between €80m (£72.4m) and €85m plus the services of the Croatian midfielder.
Dybala has also been heavily linked with Barcelona since the departure of Neymar. However, recent reports in Spain have claimed that the club have put the interest in the Juventus forward on hold with Ernesto Valverde having identified Liverpool star Philippe Coutinho and Borussia Dortmund's Ousmane Dembele as his two main priorities to replace Neymar.
The news regarding Real's interest may put Barcelona on alert after a recent poll conducted by Catalan publication Mundo Deportivo revealed the Juve forward is eventually the supporters' preferred candidate to replace Neymar ahead of Dembele, Atletico Madrid's Antoine Griezmann and Mbappe.
Furthermore, Mundo Deportivo had previously reported that Barcelona have a first option on Dybala and could acquire him for around €120m thanks to a special clause insisted by the player when he signed a new deal at the club in April.
Barcelona have already seen themselves involve in a number of battles with Real during the current summer transfer window. The Nou Camp club tried to sign Dani Ceballos, Theo Hernandez and Vinicius Junior before they opted to move instead to the Bernabeu.