The England international's current deal is due to expire at the end of the season but he hopes to impress enough to earn an extension, and has hailed the return of Jose Mourinho
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."