Cole has been at Stamford Bridge since 2006 and was the subject of speculation with a move to Real Madrid before the Spanish giants signed Benfica's Fabio Coentrao.
The England international says the club was disappointed with going so close last season only to fall short in all competitions, but he has no intention of going elsewhere to seek success.
"It was disappointing last season, although we came close only to fall at crucial stages," he told Sky Sports.
"We hope to win something in the new season. I want to end my playing career with Chelsea.
"There are still many more years of football in me and I want to be part of Chelsea as this is the club that can pose a threat to all the big names in the game at all levels."
Cole also revealed that new manager Andre Villas-Boas has already impressed the squad with his methods.
"We have a young manager who is somewhat on the same wavelength with the players. This is wonderful to the team," he said.
"When we train and if we are tired the manager will stop the training and move on to other things to add spice to our training sessions. This has been good and we have come on fine so far."