Douglas is under contract with Gremio until 2013 and has a £22million clause.
The highly rated youngster has also been linked with Champions League winners Manchester United.
“I am delighted that such a big club as Real Madrid are interested in me,” Douglas told Marca. “This fills me with pride and makes me understand I am doing good things.
“Such a prestigious club being interested in a player like me is unusual because I do not have much first division experience.
“So I am hopeful I will be able to show them my gratitude one day while wearing the famous white shirt.
“For sure I would like to play for Real Madrid! Despite me owing everything to Gremio, playing at the Santiago Bernabeu would be fantastic.
“I have just turned professional but I never doubted of my qualities. I would describe myself as a left midfielder with many [technical] qualities, quick, that loves to touch the football and organise the game.”
