The centre-back - who is fit to face Atletico Madrid in the Champions League semi-final second leg at Stamford Bridge - wants to end his career at Stamford Bridge
Terry is out of contract at the end of the season but has rediscovered his best form under Jose Mourinho, and the 33-year-old has made no secret of a desire to remain with the club.
And the centre-back is now waiting to see whether he can be granted his wish to remain at Stamford Bridge.
"I want to stay here for the rest of my footballing days," the Chelsea captain told reporters. "It's the club I've been at since 14 and I've been nowhere else.
"We're in talks. We've had big games, so we haven't spoken for a few weeks, but I hope it gets done.
"It's down to the club but I want to stay and I hope something gets sorted out."
Terry has handed Mourinho a huge boost ahead of the second leg of the Champions League semi-final clash with Atletico by declaring himself fit after recovering from the ankle injury that forced him to sit out Sunday's victory at Liverpool.
He said: "On Sunday I went out and trained with the boys who stayed back and it was totally fine. [On Monday] I did a full session and I did again [on Tuesday], touch wood I've had no problems."