Cole signed a new one-year contract with the Blues last season, but is hoping that he can stay with the Europa League holders, whom he joined from Arsenal in 2006, beyond his present deal.
However, the England international full-back has acknowledged that his time at Chelsea may come to an end in the near future, and believes that his current understudy Bertrand is the man to fill his shoes.
He told reporters: "I signed an extension at the start of the year and so have this year left and it will be up at the end of the season. I hope to stay for longer. I have had a great time here, a great career here and, of course, I'd love to stay if they still want me.
"There is going to be a time when they will have to replace me. I have Ryan [Bertrand] in my place and one day I'm going to want to watch him play, so the time will come when I do finish my career."
Bertrand, 24, has made 57 appearances for Chelsea in all competitions, including a start in the 2012 Champions League final, since debuting in 2011.