Real are expected to clinch the 17 year-old's signing after bidding €45m for the striker last week. Rivals Barcelona have offered €30m.
Meanwhile, UOL Esporte says should he choose Real, Rodrygo will go to Madrid on a salary of €4m.
The youngster will be eligible to move to Europe when he turns 18 in January 2019.
For the moment, Santos refuse to sanction Rodrygo's sale, referring Real to his €50m buyout clause.