Terry has experienced a resurgence in form under Blues boss Jose Mourinho, but will be out of contract at Stamford Bridge when his current deal expires in the summer.
"I think when the manager speaks about forever I agree," Terry said, according to The Express. "I've been here since I was 14 and nowhere else. I want to stay here for the rest of my footballing days.
"We are still in talks which are ongoing, because of the big games recently we haven't spoken for a few weeks. But I hope it gets done as I want to stay.
"I hope things can be wrapped up by the end of the season. It's down to the club. They know I want to stay."
Chelsea currently occupy second position in the Premier League table.