The Reds defender was forced off during Wednesday night's 1-0 defeat at Arsenal after tweaking his groin and has been ruled out for seven to 10 days.
Carragher is doubtful for next Thursday's Europa League clash with Romanian champions Unirea Urziceni at Anfield and Rafa Benitez will take no chances with his vice-captain ahead of the potentially season-defining contest at Eastlands.
The manager's major concern will be ensuring Carragher is ready to face Roberto Mancini's side.
Manchester City pose the greatest threat to fourth placed Liverpool's hopes of Champions League qualification and if the 32-year-old was to miss out it would be a huge blow.
As Carragher focuses on a speedy return to action, Torres is stepping up his rehabilitation at Melwood.
The Spanish striker, who has been out since he suffered a knee injury in the FA Cup defeat to Reading a month ago, has started running again.
When the Reds' 12-goal top scorer underwent surgery to repair torn cartilage he was told he would be missing for six weeks.
Benitez is reluctant to put a time frame on Torres' return to action and will resist the temptation to rush him back.
The manager intends to monitor his progress over the next week before deciding whether he's capable of playing a part against City.