The Germany international has allegedly agreed terms with HSV and will leave his current club on a Bosman move in the summer after losing his place in Robin Dutt's side
HSV are in the market for a new keeper as they are thought to be disappointed with the performances of Jaroslav Drobny between the sticks, and head coach Thorsten Fink sees the 27-year-old Adler as the perfect signing.
The glovesman has lost his starting berth at Leverkusen to Bernd Leno after a serious knee injury, and is keen to re-launch his career elsewhere.
Adler has an expiring contract with Leverkusen and talks over a new deal broke down earlier this season.
Therefore, he is expected to leave the club on a Bosman move at the end of the 2011-12 campaign, and Hamburg are expected to officially announce the capture of Adler in the coming days.