The 32-year-old's deal with Jose Mourinho's side is due to expire at the end of the season, but the left-back believes he still has a lot to offer the reigning Europa League champions.
|9/4||Chelsea are 9/4 with Coral to win the Premier League|
"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."
Chelsea sit in second place in the Premier League table, with Cole featuring in eight of his side's nine league outings, and the full-back believes the west Londoners are well-placed for success under Mourinho.
"He's come back to the club where he did a fantastic job winning two titles," Cole added.
"He always demands 100 per cent whether it's in a game or in training. He always wants the best, he always wants your best.
"He's a fighter and a winner and he wants to go into every game and win, just like us players."