VfB are seeking a new head coach after sacking Pellegrino Matarazzo on Monday following nine games without a win.
Sky Deutschland says Stuttgart have already opened talks with Low about the job, with contact initially made on Monday night.
Low, 43, has previous coaching experience in the Bundesliga with RB Leipzig, where he was an assistant between 2015 and 2018.
He lost his job at Chelsea in September after the sacking of manager Thomas Tuchel.