The club's sporting director has confirmed he would be keen to offer the Switzerland international a deal to remain in the Bundesliga following his loan with Hannover
Djourou made just two Capital One Cup appearances for the Gunners last season but appeared 14 times in the Bundesliga after moving to Hannover on loan in January.
Mirko Slomka's men were reportedly hoping to retain the Switzerland international after finishing ninth in the table, but Hamburg sporting director Oliver Kreuzer has revealed his club are keen too.
"We would loan him, but we would also buy him, depending on what Arsenal prefer," he told Bild.
"Johan embodies the style we are looking for.
"He plays the ball constructively forward from the back. He is fast, good at heading and can lead. Plus, he will just reach his best age as a football player.
"Hannover played some good matches in the Europa League recently. But Hamburg is Hamburg and HSV is HSV."