The 35-year-old – who has spent his entire career at Chelsea, making almost 700 appearances, apart from a brief loan spell at Nottingham Forest when he was a teenager – has been the most successful skipper in the club’s history.
“It’s not going to be a fairytale ending, I’m not going to retire at Chelsea,” said Terry after his side’s 5-1 win over Milton Keynes Dons in the FA Cup fourth round.
Terry met with Chelsea powerbrokers before last week’s EPL game against Arsenal to discuss whether his contract would be extended.
“I needed to know now like I have done every January and sometimes it takes a couple of months to get done,” he said.
“Unfortunately, it was a no. It took me a couple of days to get over.
“I want to give everything and finish on a high. I couldn’t play for another Premier League club, it will be elsewhere for sure.”
Chelsea were not immediately available for comment.
Terry, who made his debut as a substitute in a League Cup tie versus Aston Villa in October 1998, has led the Blues to victory in the Champions League, won four Premier League titles, five FA Cups and three League Cups as well as the Europa League.
He also played 78 times for England, scoring six goals.
Last season when Chelsea won the title, he played every minute of every league match.
That run ended when he was substituted at halftime in the second game of this season by then-manager Jose Mourinho in a 3-0 loss at Manchester City.
He was then sent off in his next game against West Bromwich Albion as Chelsea’s early season woes continued, culminating in Mourinho’s departure in December.
Terry’s form may have dipped this term but a glimpse of what he means to the fans came when he equalised late in stoppage time to force a 3-3 draw with Everton last month to preserve Chelsea’s unbeaten run under interim coach Guus Hiddink.
Jumping on to the hoardings surrounding the pitch to celebrate, he was almost engulfed by the adoring supporters.
However, Terry has not been universally popular in England with a series of controversies during his long playing career.
In November 2011, he was investigated by the police and later the Football Association for alleged racist abuse against Anton Ferdinand of Queens Park Rangers.
Although Terry was later acquitted in court, he was banned by the FA for four matches.
He was twice stripped of the England captaincy and also fell out with former Chelsea teammate Wayne Bridge, who refused to shake his hand before a match following media allegations that Terry had an affair with one of his former girlfriends.
Meanwhile Chelsea, beginning to find their form under Guus Hiddink after a shocking start to the season, will face Manchester City in the outstanding tie of the FA Cup fifth round following Sunday’s draw.
Hiddink won the FA Cup with Chelsea during his first spell as interim manager in 2009 and has seen them improve since the sacking of Mourinho.
They stretched their unbeaten run to nine matches with the 5-1 drubbing of second-tier side Milton Keynes.
City are bidding for the title as well as seeking success in the Champions League and League Cup, where they face Liverpool in the final, and also enjoyed an easy away win with a 4-0 success at Aston Villa on Saturday.
Holders Arsenal, bidding to become the first team since 1886 to win the FA Cup for three years in a row, will meet Championship side Hull City in the competition for the third year running.
Arsenal beat Hull 3-2 after extra time in the 2014 final, having trailed 2-0 after eight minutes, and retained the Cup last season after starting their defence of the trophy with a 3-0 win over Hull in the third round at the Emirates.
The last club to win the FA Cup for three years running, and the last team to defeat Arsenal in the competition in 2013, were Blackburn Rovers, whose reward for beating Oxford United 3-0 on Saturday is a home tie against Liverpool or West Ham United.
The second-tier side will play the winners of next week’s replay after the pair drew 0-0 at Anfield on Saturday.
Shrewsbury Town, battling against relegation from League One, scored two late goals to beat Sheffield Wednesday 3-2 on Saturday and are rewarded with a glamorous home tie against Manchester United, whose 11th and last triumph came in 2004.
It is Shrewsbury’s first appearance in the fifth round since 1991 which was also the year eight-times winners Tottenham Hotspur last lifted the trophy.
Spurs will be hoping to take another step towards ending that long wait when they face Crystal Palace in a London derby at White Hart Lane.
Twelve top flight teams are left in the competition and, as well as the Chelsea v Manchester City and Spurs-Palace ties, Bournemouth will take on Everton, 3-0 winners at Carlisle United on Sunday, in the other all-Premier League clash.
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