The 24-year-old Croatian has a contract until 2025 but there is speculation about his future ahead of the January transfer window.
There are claims that he could be forced to leave in January as Stuttgart need money, but the club would rather keep hold of the defender if they can.
Sosa is claimed to be preferring a move away from Stuttgart next summer instead of January and several clubs are interested in him.
According to German daily Bild, Newcastle are amongst the clubs who are keeping tabs on the player, who will be in the shop window at the World Cup.
Eddie Howe wants to bring in a high-quality left-back and Sosa has been identified as a potential target.
However, Newcastle are likely to face Italian competition as Inter Milan and Atalanta are interested in him as well.
It has been claimed that Bayern Munich coach Julian Nagelsmann is also a big fan of the Croatian.
There are suggestions that a good World Cup could lead to the prospect of Sosa leaving in January as well.