Pavard is regarded among Europe's best young defensive talents now emerging.
The French youngster, 21, has not missed a Stuttgart first team game this season and his progress has attracted attention from abroad.
The defender, who joined VfB in 2016 from Lille, has a deal to 2019 and recently put off new contract talks.
He said earlier this season: "I do not know anything about the interest of other clubs. Good things come to those who wait for it! At the moment I feel very comfortable in Stuttgart and I want to stay competitive with VfB. I was allowed to show myself in the national team, it's something! I am known now. In the next few months, I will have to confirm with Stuttgart."