The Gunners youngster has impressed at Euro 2016.
Despite his initial promise, Gnabry's progress at the Emirates Stadium has stalled in recent seasons and the 21-year-old was farmed out to West Bromwich Albion last season, where he played a mere 12 minutes of league football.
However, Gnabry has shone for Germany's Under-23s at Rio 2016, scoring six goals to lead his country to a semi-final date with Nigeria.
The report claims his displays have caught the eye of several clubs back home, with Hertha Berlin the first to publicly declare their interest.
"Serge exactly meets our search parameters," Dardai is quoted as saying. "Let's see what will happen in the next couple of days."
Gnabry recently entered the final year of his Arsenal contract and the Gunners could look to cash in on the player they signed from Stuttgart as a 16-year-old.
However, with Alex Iwobi ruled out for a month, Gnabry may finally get another chance to impress upon his return to the club next week.
Should the German move to Hertha this summer, he would link up with Liverpool loanee Allan and former Chelsea forward Salomon Kalou at the Berlin Oympiastadion.