The England striker is yet to feature for the Hammers this season after suffering a problem with his foot which has needed treatment from some of the top specialists Europe and the United States can offer.
Reports suggested Carroll could return to training after their clash with Swansea on Sunday but Allardyce was quick to quash any rumours.
"The stories that Andy Carroll is returning to us this week are not true," the West Ham boss said.
"There is still a while to go there. He'll be back we hope in the next two to three weeks. Hopefully he can start full training when he does come back. It's always been a week-by-week assessment.
"He is frustrated of course and is desperate to be playing football again, it's what he loves doing most. I will only be too pleased to get him back in the squad."
West Ham's other forwards have struggled for goals in Carroll's absence and Allardyce played without a recognised striker in their last two games, a 3-0 win over Spurs and a 3-1 defeat at home to Manchester City.
"It's worked very well in the first game, not so well in second," he said. "It will be our choice in the next few days about whether we change the system.
"Carlton Cole played another under-21 game last Monday. Our under-21s are top of the league, that's great news from the younger end.
"I don't think Cole is ready to start from a match fitness point of view but his experience from the bench is invaluable at the moment."