Cole, 27, ruptured his anterior cruciate ligament in Chelsea's 4-1 win over Southend United in an FA Cup third round replay on January 14.
He has since undergone surgery and although he has no chance of playing again this season, is happy with how his recovery is going.
"There was always a dream in my head of a possible Champions League or FA Cup final but the physios put the kybosh on that every time I mentioned it. So my comeback target is going to be pre-season for the start of next season," Cole told Chelsea TV.
As well as missing Chelsea's run-in over the second half of the season he will also miss England's upcoming World Cup qualifiers against Ukraine, Kazakhstan and Andorra, as well as the friendly against Slovakia later this month.
However, he told the channel: "I am ahead of schedule. The physios are really happy with me and how I feel at the moment is how I am supposed to be feeling. There is obviously a bit of muscle wastage in the legs so I am working on that but I am pleased."
Cole is one of three Chelsea players to have suffered cruciate ligament damage this season along with Michael Essien and Paulo Ferreira.
Ferreira suffered his injury in training last week while Essien played on Saturday for the first time since last August when he appeared as a second-half substitute in Chelsea's 2-0 win at Coventry City in an FA Cup sixth round match.
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