The huge 23-year-old is currently with the Germany Under-21s side as they prepare for the EURO U21 final against England on Saturday.
Woltemade has been his side’s main man throughout the tournament, scoring six goals and providing three assists in his five games.
As a result, Bayern Munich acted quickly to reach an agreement with the striker amid interest from the likes of Chelsea.
Stuttgart have no intention of letting their young star leave any time soon, however, and are insistent he remains a key part of their plans.
Stuttgart’s sporting director, Wohlgemuth, addressed the ongoing transfer rumours: "The fact that this development hasn't gone unnoticed by others and that we now read about interest from other clubs almost every day doesn't change the fact that Nick's journey with us is far from over," he told Bild.
He then added: "We are firmly committed to Nick and want to continue to benefit from his athletic qualities in the coming year. There is no alternative planning scenario."