Carroll has yet to feature this season because of an ankle ligament problem and has endured miserable luck since joining West Ham from Liverpool for a club-record £15 million fee in June last year.
The former Newcastle United forward has made just 16 appearances for the Upton Park club since making his move to east London permanent following a loan spell with Allardyce's men the previous season.
But Allardyce has now indicated that the 25-year-old could finally make his comeback in the near future, although he expects Carroll to be wary of picking up another injury upon his return to the fray.
"He's training away. It'll be another two or three weeks if he has no niggles of problems," Allardyce said.
"We'll try to get him through three or four behind-closed-doors games and if that goes alright then we would hope to have him back.
"It's been a long, hard road again for Andy and one he's been too familiar with recently, sadly. Hopefully, when he gets back, he'll have a major impact.
"As we all know, training is fine, but we've got to get some game time into him before we really put him back into the squad.
"You always get fearful when you first come back until something happens that makes you just go and play.
"There's always a little bit of fear factor when you come back from a long injury. With the medical staff, the guidance, the strength and conditioning work, it all ends up being psychological in the end."
