The striker scored a hat-trick last weekend to take the Gers to the top of the Scottish Premier League for the first time in 10 months.
Defoe has now scored 12 goals in 14 appearances this season and has now sent a message to Bournemouth about his future.
"I want to stay," he told Sky Sports. "It's a special football club - you feel it."
Now 37, Defoe was then asked if he could extend his career into his 40s, Defoe says: "The way I feel now, easily.
"I do everything right [to prepare for matches], which is easy for me. My recovery, training, knowing how to manage myself. All the things you should do, I do. I think it's showing in my performances."