Cole missed England's final two World Cup qualifiers with a rib injury and has been unable to train ahead of Saturday's match at Stamford Bridge.
Jose Mourinho also confirmed Ryan Bertrand will start at left-back in Cole's absence.
“Ashley is not selected. I don’t know [when he will return] – it depends on the pain," Mourinho told reporters.
“It’s not dangerous but it’s very painful. At this moment the pain persists and he can’t train.
If he can train on Monday and be a choice for Champions League – I have my doubts.”
Schurrle will miss the clash against Cardiff with a leg injury he sustained whilst on international duty with Germany.
The 22-year-old scored a hat-trick for Joachim Low's side in their 5-3 win over Sweden on Tuesday but Mourinho insists he is happy with the other options he has at his disposal, despite the German forward's recent form.
“It’s a kind of problem that happens a lot in World Cup years,” Mourinho continued.
“A player with a little problem wants to play for his country and returns to the club.
“He has a little problem in a [leg] muscle and we cannot risk. It’s no problem because he was in very good form.
“We have other players and options. It’s not a problem. It’s a position where we have good enough problems. It’s a chance for someone else.”
Torres suffered a knee injury during Chelsea's 4-0 victory over Steaua Bucharest on October 1, but Mourinho has revealed the Spaniard is in contention to start and is competing for a place alongside Samuel Eto'o and Demba Ba.
“He’s ready. The medical department are good and the player is very good. Good dedication. He’s back," Mourinho said.
“We have the three [strikers] available. I want to have problems by having players to choose.
“I don’t want an easy selection. I want a difficult selection. [Fernando] Torres, [Samuel] Eto’o and Demba [Ba] are all ready.
“He could start. I was doing tactical work but I was not wanting to show the player who is going to play. They don’t know who is going to play.”
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