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.
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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.”