The 22-year-old has been one of the standout players at the World Cup and scored twice for his country in their 2-0 win over Uruguay on Saturday.
Rodriguez's recent displays have seen him linked with a number of Europe's biggest clubs, and Carlos has urged Madrid president Florentino Perez to bring him to Spain this summer.
"He is at Monaco, which is a great team, one of the best in France, but if we have a word with Florentino who knows what might happen, Florentino can do anything he likes," Carlos is quoted as saying by the Daily Star.
"Rodriguez is very good - he has already shown that at Monaco. I follow the leagues around the world and I have seen him play at a high level in France."
Rodriguez is the leading goalscorer at the World Cup with five goals.