Havertz suffered a knee injury in the first game of the season and underwent a minor procedure days later.
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Gunners boss Mikel Arteta was hoping to have Havertz available after this international break.
But Nagelsmann stated on Tuesday: "Kai (Havertz) had a minor relapse, but overall he’s doing well."
He also added that he believes Arsenal will be able to call upon the star '"towards the end of the (calendar) year."