The German is leaving his post in charge of the national team after the conclusion of Euro 2024.
Naglesmann is said to want another club job, given he is still only 36 years old.
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According to SPORT1, he has been approached by a Premier League club in recent weeks.
Whether that team is Manchester United is not clear, given Erik ten Hag is still in charge.
If United do want to hire Naglesmann, they may have to move quickly to secure their man.