By FOX Sports Staff
Marca sources in Germany claim Real have taken notice of Draxler's performances for Schalke in both the Bundesliga and the UEFA Champions League.
Schalke currently occupy fourth spot in the Bundesliga and were cruelly beaten by Galatasaray in the last-16 of the Champions League 4-3 on aggregate.
The Spanish newspaper reports that a number of European clubs are monitoring the player and that Schalke will fight hard in the summer to avoid losing "one of the jewels in its crown".
"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," Draxler told Marca.
"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 Classicos."
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."
In the meantime, the 19-year-old is fully focused on guiding the club back to the Champions League next season.
Schalke recovered to claim a 2-2 draw against Bayer Leverkusen over the weekend to keep them a point clear of Freiburg in the race for the final Champions League berth.
Leverkusen went 2-0 up near the hour mark after goals from Simon Rolfes and Michal Kadlec but were pegged back twice thanks to Teemu Pukki and a penalty from Raffael.
With five games of the season to play, the Royal Blues have their destiny in their own hands and travel to fifth placed Freiburg on the final day of the season.
"We've not lost and we're still only four points behind [Leverkusen], which we can still bridge," Draxler told Sky television.
"Freiburg must not be underestimated for sure, but I would say that the current top four will be playing in the Champions League next season."