Cole has undergone an operation to repair his fractured left ankle.
A source close to Cole told News of the World: “Ash is incredibly optimistic about being fit in time for the World Cup.
“Obviously he was devastated when the scan showed that he had fractured his ankle.
“He was very down for a day because England and the World Cup mean everything to him.
“But the operation went very well and the prognosis was more positive than negative, which is good news for him.
“The fact is Ashley is naturally very fit and has shown in the past he recovers quickly from injuries.
“His rehabilitation programme will start as soon as possible and he’ll be doing everything he can to be fit for both Chelsea and England.”