The 21-year-old was linked with a number of big European teams during the summer transfer window, including Manchester United and Monaco.
Despite reported interest from elsewhere, Bobic is hopeful that the Bundesliga outfit can persuade the German international to stay put at the Mercedes-Benz Arena.
"Rudiger is a first-team player of our club," he told TZ. "There are many attempts from clubs to persuade him to leave our club, and it's definitely not an easy thing for the player to resist these offers.
"We have said we are out to keep him at Stuttgart and it will be tough. Still we want to hand him a great future at our club."
Rudiger has won two caps for the German national team after making his debut earlier this year.