Rodrygo, who joined Real Madrid in a €45m (£38.5m) move from Santos in 2019, has struggled for game time at the Spanish club this season, and Spanish newspaper El Nacional report the Los Blancos would be willing to cash in on the Brazilian if they can make 'significant' profit on him.
El Nacional claim Liverpool tabled a €60m bid for Rodrygo in the summer, but Real Madrid rejected it, as they hoped the Brazilian would have an important role under Carlo Ancelotti.
That has not been the case so far this season, although he has shown glimpses of his potential, with two goals and three assists to his name in the ongoing campaign.
The Spanish newspaper further claim Liverpool could look to reinforce their squad in the January transfer window, as the likes of Mohamed Salah and Sadio Mane could leave the Reds for up to a month for Africa Cup of Nations.
Meanwhile, Real Madrid president Florentino Perez is convinced the money they spent to sign Rodrygo was a 'good investment' but the Spanish club would consider selling the Brazilian if a good offer arrives, one where they can make significant profits.