Boateng joined Spurs last summer from Hertha Berlin, but has been unable to establish himself as a first-team regular.
He has made 21 appearances for the club, but is being offered a return to the Bundesliga for next season.
Stuttgart's general manager Horst Heldt has confirmed the club are looking to settle on a deal for the former Young Player of the Year.
Heldt told Bild: "Boateng is a very interesting player. We are in talks."