Norgaard joined Arsenal in June 2023, signing a two-year deal with the option of a third year, following a £15m transfer from Brentford.
The Denmark international is currently a backup player for manager Mikel Arteta, having made 122 Premier League appearances for Brentford since helping them win promotion in 2021.
Norgaard has stated that he would be happy to extend his stay at Arsenal for another year if circumstances allow, but has also expressed a desire to return to his former club Brøndby when his contract expires.
Brøndby would welcome Norgaard's return, bringing his experience and skills back to the team after a seven-year absence.