It had been reported that the 27-year-old had agreed terms with Wolfsburg, with his Bremen deal expiring at the end of the season.
However, his representative Karl-Heinz Forster has revealed that contract talks with his current club are ongoing.
"In terms of Aaron, Werder Bremen will remain the main partner of conversation regarding his expiring contract," Forster told Bild.
"I am sure there will be contract talks come the Bundesliga's winter break. There have not been any talks with Wolfsburg or any other club thus far. Those reports are pure speculation."
Hunt joined Bremen in 2001 before making his first-team debut in 2004.