The Germany international, who is currently Bremen's vice-captain with 174 appearances to his name, is out of contract in June 2014.
However, the 27-year-old has confirmed he is not ready to pen a new deal at the Weserstadion yet.
Hunt, who has a German father and English mother, has been linked with Premier League clubs - most notably Stoke City in the transfer window - but remains tight-lipped on his future plans.
"I am fine and I have a contract to end next summer," he told the Weser-Kurier.
"Thus far I have not scheduled any contract negotiations with Werder Bremen for the near future.
"I will at first wait until the January transfer window is approaching."
Hunt joined Bremen's academy at the age of 15 before progressing through the ranks to become a first-team regular, where he has scored 35 goals.