The newspaper reported that the current expectation at the Bundesliga club is that the 25-year-old midfielder will stay beyond the summer. Stiller is currently with Germany at the World Cup, where he has established himself as a regular in midfield under Julian Nagelsmann.
His contract at Stuttgart runs until 2028, a deal that includes a release clause set at €36.5m. That figure would represent a significant fee for a player who joined Stuttgart from Hoffenheim in 2023 for a reported €5.5m.
However, VfB Stuttgart retain the right to buy out the clause entirely for a fee of just €2m, a mechanism built into the contract when it was extended. That arrangement gives the club significant leverage, allowing them to remove any fixed exit route for the midfielder regardless of his form at the World Cup.
Stiller has become an increasingly important figure in Sebastian Hoeness's midfield since arriving at the MHP Arena.
He has also broken into the German national team picture, making his senior debut under Nagelsmann's predecessor before becoming a regular fixture in the squad.
Reports earlier this year linked Manchester United, Chelsea and Juventus with potential moves for the midfielder, with United in particular said to have explored triggering his release clause before the tournament.
Stuttgart's decision to retain control over his future, rather than allow a fixed-fee departure, reflects the value the club places on the midfielder regardless of outside interest.
For now, Bild's report suggests no departure is imminent, with Stiller's focus firmly on Germany's World Cup campaign rather than any transfer speculation.
Should Germany progress deep into the tournament, and should Stiller's performances continue to draw attention, Stuttgart's position gives them control over any negotiations that follow once the World Cup concludes.
For a club that has built much of its recent identity around developing and then profiting from key midfielders, holding on to Stiller for at least one more season would represent a deliberate change of approach, banking on his World Cup form to drive his value even higher before any sale is considered.