The 25-year-old has become an increasingly important figure at Stuttgart since joining from Hoffenheim in the summer of 2023. Stiller scored two goals and provided eight assists in 52 competitive matches for Stuttgart last season.
He is contracted to the Bundesliga club until the summer of 2028, having extended his deal in January 2025.
Barcelona, Juventus, Real Madrid, Liverpool and Manchester United have all been credited with interest in Stiller over the course of the season.
Newcastle United now join that list, with Kicker reporting the Premier League club are showing concrete interest in the midfielder.
Stiller came through Bayern Munich's academy before joining Hoffenheim on a free transfer in 2021, where his best season yielded two goals in 26 appearances.
He moved to VfB Stuttgart for a fee in the region of €5.5million in August 2023, a transfer that has since paid off handsomely for the Bundesliga club.
His market value has climbed sharply since the switch, now estimated at more than €42million. Stiller made his senior debut for Germany in September 2024, coming on as a substitute in a 5-0 win over Hungary.
He went on to earn a first World Cup call-up from Julian Nagelsmann this year, having won nine caps for his country.
Stiller has also lifted major honours earlier in his career, including the Champions League and Bundesliga title during his time in Bayern Munich's system.
Newcastle finished twelfth in the Premier League last season and will be eager to strengthen their midfield options as they look to push back up the table.
Any move for Stiller would represent a significant step up in profile for Newcastle, given the calibre of clubs already tracking the German international.