"I want to leave Chelsea. Something is broken with the club," the 29-year-old striker told the magazine.
The west London club were quick to dismiss the idea of a possible transfer.
"Didier Drogba signed a new four-year contract last year. As a top professional we are sure Didier is committed to Chelsea and intends to honour that contract," the club said on its Web site (www.chelseafc.com) on Thursday.
The Ivorian was one of the players most affected by Portuguese manager Jose Mourinho's shock departure last month.
The coach, who led Chelsea to back-to-back league titles in 2005 and 2006, along with two League Cups and the FA Cup, has been replaced by Israel's Avram Grant.
"I can't hide the fact I've taken this whole business very badly, probably because I made the mistake of allowing too much of an emotional attachment in my relations with the coach," Drogba told France Football.
He added: "I can only say I have been unpleasantly surprised by some people."
Drogba also indicated in the interview that Chelsea had not been his club of choice after leaving Olympique Marseille in 2004 and that he had long considered a move from Stamford Bridge, despite the team's success.
"Ever since I arrived, I've been mulling a lot of things over, because I hadn't chosen my destination. My relations with Chelsea have always been bizarre.
"Right from the very first day, I wanted to leave. And every summer after that. But, despite that, I've stayed here for four seasons, the best of my career."
Drogba had added that he would like to play either in Italy's Serie A or Spain's Primera Liga.