The Times says the prospect of a coaching role was discussed before he signed his previous contract two years ago and that option still holds considerable appeal.
"I've been at the club for 14 years and never want to leave," Terry said. "I'm delighted it's all been resolved and things can be settled now.
"I've said before that management's a possibility, but I've still got a good few years ahead of me playing-wise. The managers seem to get under quite a bit of stress in the game, so I'll let them manage and just concentrate on my football."