Bremen are struggling at the wrong end of the table and, for the third year in a row, look likely to miss out on a place in Europe next season.
Should there not be any sign of an improvement in the remaining eight matches of the season, or next term, the former Germany international admitted he might have to consider requesting a transfer.
"I have always stressed that I am happy with Werder and the club has a place in my heart, but it's not certain that I will stay here and end my career here," he said.
"I have certain expectations and my future will be dependent on them."
The 26-year-old has admitted his concern for the rest of the season after a return of just two points from their last five games left them closer to the relegation zone than the top six.
"We have got to watch out that we don't fall any further," he told Kicker magazine.
"Six points is not a great advantage over a strong Augsburg side. We have ruined our chances of keeping in touch with the European places in our last three or four games."
Hunt has played 178 times for his only professional club, whom he joined in 2001, while he has been capped twice by Germany.