The Imtech Arena outfit are somewhat short of quality at the back and they believe the talented defender would be an instant hit at HSV.
They are, therefore, looking to sign Badstuber on a season-long loan, but club officials have a lot of persuasion to do if Bayern are to let go one of their key players.
Badstuber has yet to return into action from a knee injury and a loan to Hamburg could help him get back into form before he can challenge for a starting berth at Alianz Arena.
With Jan Kirchhoff set to arrive in the summer transfer window, competition for starting places in defence at Bayern will be fierce next season, and HSV officials hope the Germany international would, therefore, be prepared to accept their offer.
Before suffering a serious injury, the 24-year-old had established himself as a first team regular for both club and country.