Hunt said his goodbyes to Bremen's fans before their season-ending 2-1 loss at Bayer Leverkusen last Saturday.
The midfielder's contract expires at the end of June and the Germany international had previously declared his intention not to extend his stay at the Weserstadion.
However, the 27-year-old has now reversed his stance, revealing that he could be tempted to agreeing a new deal.
"If (director of sport) Thomas Eichin wants to talk with me, then I will talk to him," he told the Bild. "Nothing is ruled out."
Hunt also insisted that he had not spoken with Miroslav Klose about a potential switch to Lazio, who have been linked with a move for his services.
"I wouldn't say anything is not interesting to me," Hunt added. "But I haven't called Miro yet."
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