The striker is being followed by the likes of Bayern Munich, AC Milan and Manchester United, with his contract carrying a 20m buyout clause this summer.
Fabian Wolhlgemuth, sporting director of Stuttgart, spoke about his future: "In the last two transfer windows the starting prospect has always been reversed and on both occasions he ended up staying.
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"Maybe we will find other points of connection or the means to convince him to stay Our table is open, the ranking is a piece of the puzzle that can lead the players to decide in our favor or against us.
"He feels at ease here."