The Schalke 04 winger is a German international but has struggled with injuries and Juventus are hoping to purchase Draxler for a cut price fee.
According to Sky Sport Italia, Draxler could be available for around €15-20 million, despite his release clause being €45 million.
Draxler has a contract until 2018 but his poor recent injury record, which saw him miss most of last season, may result in Schalke being open to selling Draxler for a smaller fee than his release clause.
Juventus and other clubs around Europe has been linked with a move for Draxler in recent years but the 21-year-old has remained loyal to the German side who he has been with for his entire career.
Draxler was part of the German side that won their fourth World Cup in Brazil last summer.