The Ivory Coast forward was quoted by France Football magazine as saying "something is broken" at Chelsea, and that he wanted to leave following last month's departure of coach Jose Mourinho.
Chelsea stopped short of denying Drogba had made the comments, but said it expected him to stay.
"Didier Drogba signed a new four-year contract last year," Chelsea said. "As a top professional, we are sure Didier is committed to Chelsea and intends to honor that contract."
Drogba joined Chelsea from Marseille three years ago and, after settling, scored 33 goals last season.
He is one of several players reported to be seeking a transfer following Mourinho's exit.