The Austrian has been in fine form for the club this season, scoring five and assisting five Bundesliga goals, and his boss believes the 23-year-old is destined for a big future.
"We are a way station for him. He will certainly play still at a very rich and very good club,” he told Bild.
"How long Marko is here, no one can say. I don't know whether he will play here for three, four or five years."
Meanwhile, general manager Thomas Eichin admitted that Arnautovic may well leave the club at the season's end, with his contract set to expire in 2014.
"Marko is the one who can make the difference. We don’t know what will happen in the summer," he said.
"At some point another club will come in for him. Then we will see what is best for Bremen and what is best for the player."