Drogba has been out of action since the Champions League final against Manchester United in May.
Chelsea boss Big Phil Scolari said: “Didier improves every day and improves every week.
“Drogba is not completely ready for the game against Manchester City but in my idea he may be possible to play 45 minutes.
“He is starting, step-by-step, to arrive in the same situation as last season.”
