Drogba was given a six-match ban, the last two games suspended for two years, for his angry confrontation with referee Tom Henning Ovrebo at the end of their Champions League semi-final defeat to Barcelona in May.
Uefa's Control and Disciplinary Body also handed a four-match ban, the last game suspended for two years, to right-back Jose Bosingwa.
But the severity of Uefa's punishment stunned the London club who have now informed Europe's governing body of their intent to appeal against the punishment.
Chelsea's message to Uefa also gives them more time to prepare their case. They now have another six days in which to lodge their appeal.
Chelsea are also expected to appeal against their fine of 100,000 euros for the improper conduct of their players and for the throwing of missiles by their supporters.
Referee Ovrebo was at the centre of controversy after rejecting four penalty appeals during the second leg of the semi-final which ended 1-1 on the night.
But Andres Iniesta's late away goal gave Barca a place in the final where they beat Manchester United to win the trophy.
Drogba's foul-mouthed rant at the official was captured by watching millions on live TV. The Ivorian stunned the worldwide audience by shouting "It's a ------- disgrace" straight at the cameras. He later apologised for his behaviour.
Bosingwa was banned for labelling Ovrebo a "thief" in an interview - words he later retracted. But he too will miss a large chunk of Chelsea's Champions League group stage unless the club can get the suspensions reduced on appeal.