Speaking at a Germany press conference during the World Cup, Leweling said: "You can never rule anything out and I wouldn't say I'm staying 100 per cent.
"But I wouldn't say I'm definitely leaving either. My focus is on the World Cup, and after that we can look further."
He then pointed to the qualities that make Stuttgart an attractive base.
"You should never rule anything out, especially not in football. Things can move quickly. But as I always say: I feel good in Stuttgart, we play Champions League and I have a good standing there."
Leweling featured in Germany's 2-1 Group C victory over Ivory Coast and has been one of the Bundesliga's most consistent wide players over two seasons. He scored seven goals and contributed nine assists in the Bundesliga last season, helping Stuttgart qualify for the Champions League for a second successive year.
VfB Stuttgart are seeking at least €50m for the winger, having already rejected a €40m bid from Bournemouth in January. Sky Germany reported three months ago that AS Roma, Everton and Bournemouth had each made concrete expressions of interest. Leweling is contracted to the club until 2029.
Bournemouth's European qualification this season puts them in a stronger position to attract players of Leweling's profile than in previous windows, and they are expected to make a second approach once the World Cup concludes.