The attacking midfielder has said he feels comfortable at the Bundesliga outfit and will not be swayed by incentives at other sides, though, talks of a new deal are premature
The 26-year-old still has 18 months remaining on his contract but Hunt insists financial incentives will not entice him away from the club.
“I have been here since I was young; I have been living in Bremen, Germany for 13 years. I have my family and my friends here," he told reporters.
"It is very important to me to feel comfortable in my environment – which is the case here. Only then I can regain my performance. That’s more important than the financial side.”
Hunt says the issue of extending his stay at Bremen has not arisen yet but says the club and him are both fine with the current arrangement.
He added: “So far, we have not talked about it - and that’s just not even planned. We still have one and a half years left. I’m in no rush and there is no pressure - and probably not for the club. The issue does not concern me yet."
When asked if he would be tempted by a move away from the club he replied: “It may be that something is coming, but that is far away.”
The midfielder has made a strong start to the season so far, scoring six goals and four assists in 15 appearances for 12th-placed Werder Bremen.