Although no one at West Ham is prepared to put a time-frame on Carroll's recovery, Allardyce suggested on Thursday that he could have his main frontman back before the turn of the year.
When asked if Carroll could be missing for the remainder of 2013, Allardyce replied: "I don't think we can say that at this moment in time.
"It's a week by week assessment now guided by the specialists who are in charge of his recovery."
"Andy's doing fine. He's recovering well now and we've set out a programme for his recovery which will hopefully not be as long as last time.
"We can't put a length of time on how long he'll be out for. We just have to see how he progresses on a week by week basis.
"He'll go to Europe for some one to one treatment which we've identified for him and which will hopefully speed up his recovery."