The 18-year-old arrived at the Bernabeu for a reported £40m from his home country this summer and has made an impressive start to life in Spain.
Rodrygo hit the headlines with a hat-trick in Real Madrids 6-0 demolition of Galatasaray in the Champions League on Wednesday.
He made his first two La Liga starts under Zinedine Zidane in the clubs last two games and already has two league goals in four appearances this season in addition to his European haul.
Hopes are high that the teenage winger has a bright future ahead of him but his old boss, former Manchester City midfielder Elano, revealed that he could have ended up at Anfield if Liverpool had been willing to fork out little extra cash.
"There was strong interest from Liverpool for the kid when he was in the youth teams and they wanted him, but the offer was low," he told ESPN, via the Mirror.
"Then the offer arrived fromReal Madrid. I had a chat with the club and I told them the kid was worth gambling on and that I would like to work with him.
"He already had this ability at a young age.
"There are very few players that are like that when they're so young. He's already mature and has a personality to his game.