“I was in (for talks) last week before the Arsenal game and it is not going to be extended,” Terry, 35, told reporters after his side’s 5-1 win at second-tier Milton Keynes Dons in the FA Cup fourth round.
“It’s not going to be a fairytale ending. I’m not going to retire at Chelsea.”
Terry has made 696 appearances for Chelsea and is the club’s most successful captain, having won four Premier League titles, five FA Cups, three League Cups, the 2012 Champions League and the 2013 Europa League.
He was named in the Professional Footballers’ Association (PFA) Team of the Season after inspiring Chelsea to last season’s league title, but his performances this season have not been to the same standard, mirroring the London club’s slide down the league standings.
He could now follow former England team-mates David Beckham, Steven Gerrard and Ashley Cole by moving to the United States.
But the centre-back, who signed a one-year contract extension last season, wants to go out in style by lifting the FA Cup for a sixth time and helping Chelsea climb the league table from 14th place.
“It’s my last run in the FA Cup, so I want to make it a good one,” he said.
“It’s a big season for me and I want to push on — not just in this competition, but in the Premier League as well.
“I knew before the Arsenal game (which Chelsea won 1-0), so mentally I’ve kind of accepted it. We just have to move on and climb the league.
“They said that when the new manager comes in, things might change. It’s a no at the minute. I needed to know now like I have done every January and sometimes it takes a couple of months to get done.”