The Premier League champions said he could be offered the chance to stay at Stamford Bridge following a meeting with the club last month.
"In that meeting he asked about the possibility of an extension to his existing contract," Chelsea said in a statement.
"John was advised that while no new deal was currently on the table, that situation could change in the coming months."
Chelsea said they had the utmost respect for Terry and everything he has helped them achieve, describing him as a "fantastic servant and superb captain".
Terry, 35, said he was leaving after the FAD Cup win at Milton Keynes Dons on Sunday.
"It’s not going to be a fairytale ending, I’m not going to retire at Chelsea,” Terry 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. It took me a couple of days to get over."
There has been widespread speculation that the former England international will move to either the United States or China and many commentators have questioned Chelsea's judgement.
"I think it's a mad decision from Chelsea, I don't understand it," former Chelsea striker Tony Cascarino wrote in The Times.
Former Chelsea skipper Ray Wilkins told Sky Sports: "He will be a tremendous loss to Chelsea and I think there was another year left in him."
A permanent banner at Stamford Bridge carries the message: "Captain, Leader, Legend" in deference to Terry, prompting the headlines: "Captain, Leader, Outcast" in The Times and "Captain, Leader, Legend, Leaving," in The Metro.
Terry has made 696 appearances for Chelsea and is the most successful captain in the club's history, leading them to the Premier League, FA Cup, League Cup, Europa League and Champions League titles.
Only defender Ron Harris and goalkeeper Peter Bonetti have played more games for the club.
Terry played the full 90 minutes on Sunday and is expected to lead the team out as usual when they face Watford at Vicarage Road in the Premier League on Wednesday.
Bookmaker Paddy Power offered odds of 5/2 on him joining New York Red Bulls at the end of the season, 7/2 on him moving to LA Galaxy and 5/1 to link up with his former Chelsea team mate Frank Lampard at New York City.
(Additional writing by Simon Jennings in Bengaluru, editing by Ed Osmond)
