The Turin-based giants are in the market for a new centre-back due to the departure of Fabio Cannavaro and new head coach Luigi Del Neri supposedly sees Tasci as the perfect replacement for the veteran defender.
Tasci is a product of the Stuttgart youth academy and has made over 100 league appearances for the Schwaben since making his official debut in August 2006.
The 23-year-old has also made several international appearances for Germany and is currently on duty at the World Cup with the Nationalelf, albeit not in the starting XI.
The defender has a contract until the summer of 2014 with Stuttgart, but his deal reportedly contains a £12.4 million (€15m) release clause. Juventus could face stiff competition from English outfit Tottenham Hotspur in the race for Tasci's signature.