The club's patience with the £24million striker snapped after he was shown a red card following his petulant flick in the face of United defender Nemanja Vidic.
Drogba had been earmarked to take one of Chelsea's penalties, but did not even remain on the sidelines to watch the drama unfold in the shoot-out.
AC Milan was the striker's favoured destination, but their failure to qualify for the Champions League next season has placed the move in jeopardy.