Cole, 32, who joined the Blues seven years ago from London rivals Arsenal, signed a one-year contract extension in January.
But with the England star's deal expiring at the end of the current campaign, he now plans on ending his career at the club.
"I signed an extension at the start of the year and so have this year left," Cole told The Sun.
"However, that 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 will finish my career."
It will mean Bertrand has at least another year to learn from the best instead of being shipped out because he isn't good enough yet for a regular starting place at Chelsea. Let's be honest here, he is still only 24 and is 8 years younger than Ashley, so he has plenty of time to make an impact.- chelseablue_no1