The 33-year-old’s current deal is set to expire in June 2012, but the Ivorian international is keen to extend his stay beyond next season.
“We've started talking and it's very interesting. Everybody knows what I feel about Chelsea and what I want,” he said.
“I will definitely be here next season. I said a few years ago that I will be here until the end of my contract, and I am here.”
Drogba has scored 95 goals in 202 games for the Blues since he joined from French side Marseille in 2004.