The Londoners announced earlier on Friday that the former England skipper, who is out of contract at the end of the season and feared he had played his last game for the club, had been offered a 12-month extension.
However, it is uncertain whether Chelsea's 35-year-old idol will agree to the deal.
"The contract extension the club have offered me is a different role and I hope everyone will understand I want to take the time to consider it carefully before making a decision," Terry said on Instagram without elaborating.
The offer of a new deal suggests Antonio Conte, who will take over as manager from Guus Hiddink after leading Italy at next month's European Championship, wants to keep the centre half.
Some fans staged a protest in the 26th minute, the number of Terry's shirt, of Wednesday's 1-1 draw at Liverpool urging the club to keep him.
"(Director) Marina Granovskaia and (chairman) Bruce Buck met with John and his agent this week and offered him a one-year contract extension," a Chelsea spokesman said on Friday.
Terry is banned for Chelsea's final game of the season, Hiddink's farewell match against champions Leicester City at Stamford Bridge on Sunday, after he was sent off at Sunderland last weekend.
'MY CLUB'
If Terry decides to stay it will lift the supporters at the end of a poor defence of the club's Premier League title.
Chelsea were one point above the relegation zone following defeat at Leicester in December, after which manager Jose Mourinho was sacked, and cannot now finish higher than ninth.
"I still want to play a couple more years and hopefully that's at Chelsea," Terry told Sky Sports earlier this week.
"I'm a Chelsea player, Chelsea's been my club from the age of 14."
He made his first-team debut in 1998 and is one of only three players to have appeared in more than 700 games for the club, the others being Peter Bonetti and Ron Harris.
Terry is the most successful skipper in Chelsea's history and has won 14 major trophies with the club.
"It would be very difficult (to replace him)," said team mate Gary Cahill. "Not only as a player but as a character in the dressing-room."
(Reporting by Steve Tongue and Ian Chadband; Editing by Ken Ferris and Andrew Heavens)
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