The 34-year-old centre-back, whose contact expires at the end of the season, has made 656 appearances in 16 years for the Premier League leaders.
"The club know my position," said the former England captain. "I want to stay. Hopefully my performances are showing that and they can keep me.
"I'll be happy to get one year and then see how it goes. I'm taking it year by year. I haven't got much choice."
Terry made his first team debut in October 1998, and replaced Marcel Desailly as club captain at the start of the 2004-05 campaign.
He is the most successful captain in the club's history, having led Chelsea to three Premier League titles, a Champions League success, four FA Cups and two League Cups.
Terry's former Chelsea and England team-mates, Frank Lampard and Ashley Cole, were allowed to leave the club once they had reached the end of their contracts.
Midfielder Eden Hazard, 24, is the latest Chelsea player to sign a contract extension, a move that has been welcomed by Terry, who added: "Hazard has just been done and that's the most important for the club."
John Terry wants to extend his Chelsea playing career by another 12 months.