Madrid have been heavily linked with a 70million euros (£55million) swoop for the 23-year-old forward, who has been one of the stand-out players in Brazil and is still leading the scoring charts with six goals, despite Colombia being knocked out in the quarter-finals.
Rodriguez, who only joined Monaco from Porto last season for a fee in the region of £38.5million, revealed he would fulfil a life's dream by moving to the Bernabeu and would relish the chance to line up alongside the likes of Cristiano Ronaldo.
He told Spanish newspaper Marca: "It's really flattering to know that a club like Madrid, of such magnitude, are interested in me. It would be a dream to sign for the team of my dreams.
"I have a great deal of respect for other clubs and admire the good football they play, but ultimately Real Madrid are Real Madrid. I've always had a thing for them.
"It's a dream, as I said, but also a privilege to play alongside players of such quality, all those world-class stars. It's my life's dream. If this finally happens, I only want to enjoy it.
"Cristiano is a great player, a superstar in capital letters. Cristiano deservedly won the Ballon d'Or, which recognises the best player in the world.
"I'm a very calm person, I try to stay calm at all times. But, to be honest, signing for Real Madrid is a different matter. I'm in the hands of president Florentino Perez," he added with a smile.
On whether he thinks he is worth 70million euros, Rodriguez said: "I don't know, I cannot talk about those things. I only do my work on the pitch. I'm not bothered about those things.
However, whether Rodriguez is able to fulfil his dream this summer remains to be seen.
He signed a five-year contract when he joined Monaco last year and the Colombian admits his future is down to the French club.
He said: "At Monaco I'm eternally grateful to (club president) Dmitry (Rybolovlev) and (vice-president) Vadim (Vasilyev) because they have given me this opportunity.
"It's a club that are building something big. Obviously it would be a dream for me to play for Real Madrid, but I will always respect my current club, who will have the last word on the matter."
Quelle surprise... Madrid is the "team of his dreams" and he is "calm". It's like transfer gossip by numbers. This kid is ticking all the boxes...- bungle1976