The 30-year-old's name had reportedly been amongst those in the frame to succeed Arsene Wenger after he was overlooked by Bundesliga champions Bayern Munich, who opted for Niko Kovac of Eintracht Frankfurt to replace their own veteran coach, Jupp Heynckes.
Mikel Arteta, Massimiliano Allegri and Nagelsmann were all said to be near the front of the queue for the Emirates Stadium vacancy, but Hoffenheim believe their coach is going nowhere having led the club to a Champions League spot for the second season in a row.
The club's director of football Alexander Rosen rejected speculation Nagelsmann could be tempted to take over at Arsenal.
"Julian Nagelsmann will be our coach next season - 100 per cent," Rosen said to Sky in Germany of Naglesmann, nicknamed the 'Baby Mourinho'.
Former Gunners captain Patrick Vieira had also been linked with the Arsenal vacancy, while outgoing Paris Saint-Germain coach Unai Emery admitted he had not been contacted about the position.
Goal, meanwhile, has learned that Arteta is currently the frontrunner for the position.
Luis Enrique, on sabbatical since leaving Barcelona in 2017, is another of the names reported to be in the frame, while Juventus coach Allegri has confirmed his intention to stay with the Serie A champions.