Terry, 34, is out of contract at the end of the 2014-15 campaign after signing a one-year deal last season.
The former England international has showed no signs of letting up in his 17th senior campaign at Stamford Bridge, scoring the opening goal as Chelsea trumped London rivals Tottenham 2-0 in the League Cup final at Wembley on Sunday.
And after helping manager Jose Mourinho to his first trophy in his second spell in charge, Terry is desperate to prolong his Chelsea career.
"I am fighting for myself and my family, and to prove people wrong," Terry said.
"It doesn't come much bigger than that. I want to give it everything.
"I don't know how long I have left. Hopefully I have a few years left but if this is my last year then I hope it will go out on a bang.
"I have my little target to play next year but beyond that, two or three years [more], I don't know."
Terry, who does not want to play for another club, added: "Certainly I am feeling great at the minute and it would be the wrong time to go.
"But there does come a point where it would be the right time to go, to say it's time to move on and people will remember you that way."
