The Germany international has caught the attention of a number of European giants and he would relish the chance to move to the Santiago Bernabeu side
The attacking midfielder has been in sublime form this season and his fine performances have not gone unnoticed abroad.
Draxler has previously been linked with clubs such as Inter and Juventus, but he seems to have a preference for Madrid.
"I have a contract with Schalke until 2016, but I'm proud that Real Madrid are keeping tabs on me. Madrid are one of the best clubs in the world and it would be a dream to play for them," Draxler told Marca.
"I have always said that I would like to play in Spain some day. I try to watch Madrid and Barcelona in action each week. I never miss the Clasicos.
"I often speak with Mesut [Ozil] about his life in Madrid. He has told me that he's very happy at Real."
The 19-year-old has scored 11 goals in 35 appearances in all competitions this season.