Milito's agent declared last week that the Argentine was ready to quit Zaragoza this summer and his priority was to join Juventus.
Juve were offering an initial £14 million for Milito, but Tuttosport says Real are set to trump the Italians with a bid in excess of £15 million for the stopper.
The Bianconeri had all but agreed terms with the player and Zaragoza, but the deal is now on the brink of collapse following Real's intervention.