Carroll scored seven goals during a loan spell at West Ham last season, but has been out of action since arriving at the Boleyn Ground in a £15m transfer from Liverpool last June.
The 24-year-old has been on the sidelines because of a heel problem since signing a six-year contract with the Hammers, but is back in training with the first-team.
The Hammers are second bottom in the Premier League having won just three games this season, and focus has turned to the absence of the club's record transfer.
Allardyce said: "We thought Andy would be fit around August. In the long term I'm convinced it will be a great thing for Andy to be at this club."
The Hammers boss admitted he was frustrated by defender Johnny Heitinga's decision to reject a loan move from Everton.
Allardyce told a London evening newspaper: "I spent three hours with him on Wednesday and everything seemed fine and rosy. For whatever reason, though, by yesterday morning he had changed his mind.
"I suspect a better offer had come his way but I can't be sure of that. Anyway, the reality is that the deal is dead."
Meanwhile, Allardyce is likely to play some of his fringe players when his team play Championship high-fliers Nottingham Forest in the FA Cup this weekend.
"A lot of the younger players will be escalated into the first team to see if they can master it, particularly in the cup on Sunday," Allardyce added.
One of those players could be Pelly Ruddock who has returned to West Ham from his loan spell at Luton, where the centre-back impressed manager John Still.
"I can't speak for West Ham but I can tell you he's a good player with good potential if he gets a chance I think he will do okay," Still said.