Nagelsmann is regarded as one of the best young coaches in Europe, with the 30-year-old having just guided Hoffenheim to third place in the Bundesliga.
Soon after Arsene Wenger revealed that he was leaving Arsenal, Nagelsmann was suggested as a possible replacement for the experienced Frenchman with the Gunners potentially going down the route of a head coach.
However, Rosen has dismissed those claims, telling Sky in Germany: "Julian Nagelsmann will be our coach next season. 100%."
Nagelsmann has taken charge of 94 matches at Hoffenheim, recording 41 wins and 28 draws.