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 three-time UEFA Club Defender of the Year.
“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,” said the former England Captain, adding that “I’m taking it year by year. I haven’t got much choice.”
Chelsea’s all-time highest scoring defender, made his first team debut in October 1998, and replaced Marcel Desailly as the club captain at the start of the 2004-05 Season.
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.
He said, “Hazard has just been done and that’s the most important for the club.”
The leading team in Barclays Premier League table host relegation battlers, Burnley FC, on Saturday.