The former Liverpool and Borussia Dortmund manager has been named Head of Global Soccer at Red Bull.
Matthaus told Sky Deutchsland: "I think Red Bull are thinking big - Jürgen Klopp is really big. All of this fits. There will be changes, he will have full support from the group. Then we will see what comes of it and we still hope to see him on the coaching bench at some point in the next few years.
"Everyone should do what they like, what they see as a task and a challenge. Red Bull is new territory for Jürgen Klopp, but Liverpool was also new territory and he accepted this task. If someone criticises him, I say: we must all be open to new things. For me this is a completely normal path. Jürgen Klopp can work for whoever he wants. The important thing is that he stays in football and that he can continue to give new impulses to football."
Matthaus added: "I think Red Bull has done a great job in Salzburg, Leipzig and New York in recent years. When Jürgen Klopp appears somewhere, of course there is a house number at the top. Klopp is someone who involves people. He can certainly help Red Bull achieve its goals. And Red Bull has big goals, I know that from personal experience."