Los Blancos are believed to have joined the race for the 26-year-old, who is apparently a target of clubs across Europe, including Premier League leaders Liverpool.
However, Sevilla have been firm in insisting that they will not be forced to sell the Croatian, and that remains the case even now that Madrid are seemingly in the picture, with Castro stressing that Rakitic is happy in Andalusia and close to extending his contract there.
He told Radio Cadena COPE: "I do not know anything about interest from Real Madrid.
"I hope that in the next week we will sit down again with Ivan and his brother and close a deal. I'm confident that Ivan will extend his contract because there is no reason to believe otherwise.
"He is happy in Seville, as are his wife and daughter. He has said that many times so I really believe that soon we will reach an agreement."
Rakitic has scored 12 goals in 39 appearances for Sevilla this season.