Drogba is Chelsea's top scorer this season but a persistent knee problem means the Ivory Coast hitman will be sorly missed against the Black Cats.
Drogba has earmarked an early operation to correct the problem so he can play in The African Cup of Nations in January.
Drogba will also miss Tuesday's meeting with Valencia in the Champions League and if the operation goes ahead also miss the titanic match against Arsenal the following weekend.
Chelsea want to protect Drogba for this match and allow him to have his operation after the match at the Emirates Stadium.
But this would mean he had less time to recover before heading off to play in Africa.
Chelsea have Salomon Kalou, Andre Shevchenko and Claudio Pizzaro to call upon to take Drogba's place .
Petr Cech is still out injured alongside Ricardo Carvalho and Paulo Ferrieia in defence.
Wayne Bridge is set to get the nod again over Ashley Cole at left back.