If the Champions League and La Liga winners were able to pull of such a transaction it would represent a major coup, as bitter rivals Barcelona are also known to be keen on the 23-year-old.
Dybala is one of their supposed targets to replace Neymar. However, Juve are insisting that they will not part ways with their star man for less than €120m.
Real's offer would likely match Juve's expectations, with Kovacic a valuable asset to acquire as well as €85m.
Los Blancos have already made two stellar additions to their squad with the arrivals of Spanish starlets Theo Hernandez and Dani Ceballos from Atletico Madrid and Real Betis respectively, but their customary blockbuster signing has thus far eluded them.
Monaco's Kylian Mbappe has been a star name consistently linked with the Bernabeu. However, Zidane's side could be about to switch their attention to another talent.