The highly-rated Germany international has been linked with a host of Europe's top clubs and Madrid are the latest side believed to be following the 19-year-old.
Draxler told Marca: "Real Madrid are one of the world's great clubs, it makes me proud that they like my style of play. I would be a dream to play at Real Madrid.
"I've always said that I would like to play in Spain. Every weekend I try to see the matches involving Madrid and Barcelona. I never miss the Clasicos."
He added: "Right now I'm with Schalke and I have a contract until 2016.
"I'm having a very good season and I'm doing very well, I've scored eight goals in the Bundesliga and I feel very happy."