Terry, who made his senior debut in 1998, is Chelsea's most successful captain, having led them to four league titles, four FA Cups, three League Cups and one Champions League crown since 2004.
Although Chelsea responded that they have not decided on the future of the 35-year-old, no new deal has been offered to him.
Terry was sent off in their Saturday's Premier League 3-2 loss at which means that he could have played his last game for Chelsea.
The defender has however revealed that he wants to stay.
“I still want to play for a couple more years, hopefully that's at Chelsea,” the defender said on Monday from Denmark where he went to watch Brondby IF, a club owned by his close friend Jan Bech Anderson.
“I'm a Chelsea player and that has been my club since the age of 14. I love Chelsea.'
After his red car against Sunderland on Saturday, May 7, Chelsea midfielder Nemanja Matic paid tribute to Terry.
"We know what he has done for this club and what he has won. All of us in the team wish him all the best for the future and of course this is not a good way to finish in a club," Matic told British media.