The 33-year-old has been linked with a move away from Stamford Bridge this transfer window, with former Blues team-mate Nicolas Anelka’s new side Shanghai Shenhua rumoured to be circling.
However, the former Marseille forward – who is currently on international duty with the Ivory Coast ahead of the forthcoming African Cup of Nations – hinted he will remain at the London club until the end of the season despite hoping to find "more fun" in football.
When asked if he wants to leave Chelsea, Drogba told France Football: “Not before next June.
“I'd like to find more fun, chills, fervour, passion and pressure on the field. Everything that makes the salt of my profession."
Drogba has scored six goals in 17 appearances in all competitions this season, trailing Frank Lampard, Daniel Sturridge and Brazilian Ramires in the scoring charts.
The striker is expected to be in the starting XI for the Ivory Coast when they play Sudan, Burkina Faso and Angola in the group stages, with their first match taking place on Sunday.
The Elephants are among the favourites in the continental tournament alongside Senegal and Ghana, and without reigning AFCON champions Egypt, who have won the competition on the last three occasions.