Arsenal and Manchester City are also keeping tabs on the Germany international, as are AC Milan and Inter Milan.
The 19-year-old playmaker has flourished since breaking into the Schalke first-team. Despite the presence of older attacking midfielder stars like Mario Gotze, Mesut Ozil, Marco Reus and Andre Schurrle, Draxler has even managed to work his way into Joachim Low's plans, earning three international caps.
German newspaper Bild claims the two Milan clubs are monitoring his progress, and the Daily Express carries quotes from Schalke's general manager Horst Heldt confirming interest in Draxler from overseas.
Heldt said: "There has always been reported interest from international clubs. And now we have had inquiries for Julian.
"But this is not a topic for us. A sale is not up for discussion."
His importance to the Bundesliga club has increased following the sale of Lewis Holtby to Tottenham in the January transfer window, and it seems they'll do everything they can to keep him in Germany.
Draxler's always been a highly-regarded talent, and he's stepped into the first-team to good effect, making 25 appearances and scoring five goals for the German club this season.
The teenager came through the young ranks at Schalke, and was fast-tracked through the German youth system to the national team - making just eight appearances for the under-18s and one appearance for the under-21s before jumping up to earn his first Germany cap.