Stuttgart are keen on bringing in a new goalkeeper as Jens Lehmann looks set to retire at the end of the season.
The Bundesliga side have previously been linked with a move for Hannover keeper Florian Fromlowitz.
Drobny has impressed for Hertha this season, but could be interested in leaving the club as he is not happy with his side’s performances.
Drobny’s contract with Hertha is set to expire at the end of the season.