The Switzerland defender spent the second half of last term on loan with Hannover, who are also reportedly keen on keeping him for another season.
"We would loan him, but we would also buy him, depending on what Arsenal prefer," said Hamburg's director of sport Oliver Kreuzer.
Kreuzer believes his side have more to offer the 26-year-old and is confident a deal will be struck.
"Hannover played well in Europe last season, but Hamburg is Hamburg," he told the Bild newspaper.
"HSV is HSV, and we are just a better club."
Djourou appeared 13 times for the Reds between January and May this year and is contracted to the Gunners until 2015.