The midfielder left Brentford for the Gunners last summer, penning a contract to 2027.
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Norgaard says after Arsenal, the Denmark international plans to return home to Brondby.
He said from Denmark's camp today: "When I have to go home to Denmark one day, it is Brøndby.
"Brøndby is a club that I got a special affiliation with when I played in the club.
"That's why I can't see myself playing for other Danish clubs."