Citing reports from Italy, the article claims Juve general director Giuseppe Marotta is considering a move for the playmaker amid interest from Arsenal and City among others.
Draxler only recently extended his Schalke contract until the summer of 2018, and the attacking midfielder has also attracted interest from Borussia Dortmund and Real Madrid.
The 19-year-old Germany international revealed his delight at the arrival of former-AC Milan playmaker Kevin Prince Boateng earlier this week, and is hailed as a hero among Schalke fans after progressing through the youth ranks.
But the report claims Juventus are eyeing up a potential move for one of Europe's most highly rated young stars.
Already a fixture in the Schalke first-team, the teenager stepped into the void left by Lewis Holtby last season and immediately impressed.
A Daily Mirror report last month claimed Schalke were demanding £60m for their top young prospect amid interest from Arsenal as the transfer deadline neared.
In the end, Gunners boss Arsene Wenger completed a club record £42.5m deal for Real Madrid playmaker Mesut Ozil - a teammate of Draxler's from the national team.
City completed most of their transfer business early in the window, but Manuel Pellegrini is also believed to be a fan of Draxler.