Carroll nearing Hammers return
Carroll, who scored seven goals on loan from Liverpool last season, has been out of action since arriving at the Boleyn Ground in a £15m transfer from the Reds in 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.
Ahead of Wednesday night's Capital One Cup semi-final, first leg against Manchester City at the Etihad Stadium, Allardyce said: "Andy Carroll is training and hopefully we'll see him on the bench in the next week or so."
Carroll could make his comeback in Saturday's crucial trip to fellow strugglers Cardiff City.
Allardyce, 59, also admitted he was pleased to receive the recent backing West Ham's co-owners, Davids Sullivan and Gold.
The pair produced an open letter which was published on the club's official website in defense of Allardyce and his backroom staff after the Hammers' descent to second bottom of the Premier League and following their 5-0 FA Cup third round thrashing at Championship club Nottingham Forest.
He said: "I'm obviously pleased by the united front we are trying to keep under these difficult times at the moment," he said.
"When it comes public from the co-chairmen it is nice to see and hear. From our point of view we are all understanding the difficult position we are in at the moment.
"We all have to work through it together in the hope that we turn it around in to a positive reaction in terms of our results.
"I wasn't backed by my last two chairman and got sacked for no reason at all.
"The day-to-day running of the football club is all I'm focused on. I keep in touch with the owners on a regular basis, it is a daily basis at the moment. I would be more worried if that communication went quiet."
With just one win in their last 13 league fixtures, West Ham are struggling for any sort of form and the 5-0 defeat at the City Ground only compounded the current run.
Allardyce said he understood why the fans would be feeling a little downbeat but once again defended his decision to field a young side at Forest.
"I have a lot of sympathy for them," he said of the supporters who traveled to the east midlands.
"All I can do is say that I was telling everybody weeks before we played Nottingham Forest that the situation we are in means I would be playing some of the young players in the team.
"We had to prioritize and I told people weeks before. It is now done and dusted and is out of the way."
The majority of West Ham's problems have stemmed from the fact they currently have only 14 fit players, with no recognized center-back available in recent weeks.
That has changed after the signing of experienced center-half Roger Johnson, signed on loan from League One club Wolverhampton Wanderers on Monday until the end of the season.
The defender could make his debut in the cup semi-final and Allardyce said: "The one big thing about Roger is his Premier League experience at Birmingham City. His height, which has been a weak point for us recently, and a desire to come and show he has still got the capabilities of coming to play at this level.
"He is not cup-tied, so going into one of the biggest games of the season for us with someone with his experience against one of the biggest sides in the Premier League is a help.
"If you look across the board at Man City, aerially we have to be very competent and Roger will be a great help in that area particularly.
"He is very determined and excited about the opportunity he has got after being basically frozen out at Wolves."