The 26-year-old has been with the Gunners since 2004, but despite nine years of service has failed to force his way into Arsene Wenger's first-team plans.
Djourou has two years left on his current contract but Arsenal want to cut their losses on the defender and have been encouraged by interest from Hamburger SV, according to The Guardian.
The Swiss international spent part of last season on loan with Bundesliga side Hannover and impressed in 14 appearances, but they are only interested in re-signing the centre-back on a season-long loan deal.
Hamburg have also been linked with a summer swoop, with the club's sporting director Oliver Kreuzer admitting that they would like to sign Djourou if the price is right.
He said: "I know Johan very well from my time in Switzerland [with Basel]. He's a very interesting player and someone you have to look at if he comes on the market.
"He'd be a great solution for us in defence. We're interested in a loan, but also in buying him."