The 35-year-old, who joined the London soccer club aged 14, told reporters after Sunday's 5-1 FA Cup victory over MK Dons that he will not be offered a new contract.
"It's not going to be a fairytale ending, I'm not going to retire at Chelsea," the former England skipper said, the UK Press Association reported.
Chelsea did not mention Terry's comments in its post-match website or social media reports.
The central defender was given a new one-year contract after last season, having been a key member in Chelsea's runaway title success, his fourth at the club.
However, his usually-dominant form fell away along with that of the team earlier this season, and manager Jose Mourinho was sacked in December with Chelsea languishing just above the relegation zone.
Terry has continued to feature under interim manager Guus Hiddink, marking his 700th career club appearance with a controversial equalizer against Everton in mid-January and also playing in last weekend's 1-0 win at Arsenal.
"Ideally I would have loved to stay, but the club's moving in a different direction," he said.
"I needed to know now like I have done every January and sometimes it takes a couple of months to get done. Unfortunately, it was a no.
"They said that when the new manager comes in, things might change. It's a no, at the minute. It took me a couple of days to get over.
"I couldn't play for another Premier League club. It will be elsewhere for sure. I don't know where."
With Petr Cech having joined Arsenal this season, following the departures of fellow stalwarts such as Didier Drogba and Frank Lampard, it marks the end of an era for the Chelsea players who had such success in Mourinho's first spell at the club and the following years.
Terry infamously missed a match-winning penalty in the 2008 European Champions League final defeat against Manchester United, but received a winner's medal four years later despite being suspended for Chelsea's unexpected success against Bayern Munich.
He has also won four FA Cups and three English League Cups, while he is the highest-scoring defender in Premier League history with 40 goals in over 470 top-flight appearances.
"I want to come back as a Chelsea supporter in years to come with my kids and see the team doing great," he said.
"It's going to be my last year and I want to go out at the top. We spoke about my legacy and coming back to the club when I finish. The most important thing now is to get us up the league."
Chelsea -- 13th in the table with 15 games to play -- faces Paris Saint-Germain in the last 16 of the Champions League next month and will take on Manchester City in the fifth round of the FA Cup.
The club has this month bolstered its defensive options, signing 20-year-old U.S. international Matt Miazga from New York Red Bulls.