The linebacker has spent 11 seasons with the AFC South side, having been drafted in 2002.
The 32-year-old told NFL.com: "It would be great to finish off my career as an Indianapolis Colt.
"I've been there my whole career, and I don't know anything different. Ideally, it would be great to stay there. But it is a business, so we'll see.
"Right now, I'm just thinking about Indianapolis until they tell me otherwise."
Freeney recorded five sacks during 2012, the second-lowest total of his career.