The 24-year-old has impressed at Anfield since joining from Inter Milan in 2013, leading to speculation of a potential switch to Barcelona or Paris Saint-Germain.
However, Ronaldo wants to see countryman Coutinho - who is under contract at Liverpool until 2020 - jump ship and test himself against some of the world's best players in La Liga with Madrid.
"I would love to see Coutinho at Real Madrid," he told Spanish radio station Onda Cero. "Spanish football is, without doubt, the best in history. It has always bought the best [players] and produced the most beautiful football."
Ronaldo spent five years at the Bernabeu, scoring 104 times in 177 appearances for Madrid to help the club to two Spanish top-flight crowns.