DiarioSport says Juve are keen to sign Saviola as early as January and have already registered their interest with Real.
Juve want to take Saviola on-loan for six months with the option of making the deal permanent at the end of the season.
The Italian giants will have to convince Saviola to quit Madrid, with the Argentina international lukewarm on the prospect of moving to Italy when first learning of Juve's interest.