“We all want the same thing,” said Terry in response to fans chanting “John Terry, we want you to stay”.
He added: “I want to stay, the club knows that, the fans know that.”
Terry is considering whether to accept the club’s offer of an extra 12 months, but are yet to comment on the exact nature of the role that has been offered.
On Friday, a Chelsea spokesman said: “With it coming so late in the season, this is a big decision for John and his family.”
Chelsea will be managed next season by Italy boss Antonio Conte, who takes over from Guus Hiddink after previous manager Jose Mourinho was sacked in December.
“This has been a difficult season, we are where we deserve to be in the league. The fans have stuck with us. Thank you,” added Terry.
“I can assure you we’ll be back fighting for this title next year. On a personal note, this has been tough for me, very emotional. Before I sign off I’d like to say thank you to Guus Hiddink. He is a great man.”
Terry was suspended for the game against the Foxes and has made 703 appearances since making his debut in October 1998.