A dismal run of seven games without a win in the Premier League has seen the London club plummet to second-bottom in the table.
Speculation over Allardyce's future has intensified and on Friday morning it was claimed in the media that next weekend's clash at fellow strugglers Cardiff City could be decisive for the former Blackburn Rovers boss.
Speaking ahead of West Ham’s FA Cup trip to Nottingham Forest on Sunday, Allardyce confirmed he had spoken to owners David Sullivan and David Gold as well as vice-chairman Karren Brady, but revealed the meeting was to discuss how the Upton Park club could turn around their fortunes.
He told reporters: "The position is that we're talking about trying to bring new players into the football club and trying to overcome the injury problems that we've got.
"In terms of my discussions with David Sullivan, David Gold and Karren Brady, when they're talking to me it's about positive action to get us out of the situation that we're in, which I'm very grateful for."
Big-money signing Andy Carroll is one of the injured players to have been sorely missed by Allardyce. However, the West Ham boss revealed the striker is now back in training and closing in on a first appearance of the season.
He said: "Andy will be assessed after every training session and he'll be out training with the lads on Friday, which he has done for a few days now.
"Andy playing football is something we have to take big care about, because he is fit from the injury but not match-fit.
"If he or any player plays too many games too soon, it can only promote more injuries - not in the same area but in different areas in terms of muscle fatigue and strains. I have to be very careful about when I play him and how often I play him.
"As soon as we can, he'll start from the bench and we'll arrange games behind closed doors to get his match-fitness up, as we will sooner or later with Ricardo Vaz Te and Winston Reid, who are both getting closer to training. Andy is the nearest at the moment."
Allardyce will give an opportunity to several young players in Sunday's clash against Championship high-flyers Forest.
And the West Ham boss revealed his frustration after Everton defender John Heitinga rejected a move to Upton Park on Thursday.
He said: "Is the Heitinga deal dead? It looks like it. I was very hopeful it was going to be sorted.
"I spent some time with him the other night. The morning after he had a change of heart."