The Hammers go into their FA Cup third-round clash with Nottingham Forest on Sunday sitting 19th in the Barclays Premier League after losing 2-1 at fellow strugglers Fulham on New Year's Day.
Allardyce has seen his squad decimated by injuries in the past couple of months, with the lack of depth a major factor in the club only picking up two league points throughout the whole of December.
And the 59-year-old, who is the only boss of a side currently in the bottom six who was in charge at the start of the season, is more bothered about bringing in new faces rather than worrying about joining the growing list of out-of-work managers.
"I talk to the board members all the time, but what I say with them has nothing to do with you," he said when asked if he had spoken to the owners following the Fulham loss.
"What happens is internal with those people as far as I'm concerned, not what happens publicly.
"If it was a crisis position we are in they would come and sack me, the position we are in is that we are talking about bringing new players in to the football club and overcome the injuries we have got.
"In terms of support from David Gold, David Sullivan and Karren Brady, at the moment when they are talking to me it is about positive action to try and help get ourselves get out of the situation we are in, which I'm very grateful for."
With Stewart Downing in contention to start at the City Ground and Andy Carroll now fully integrated in to training with the rest of the squad at the club's Chadwell Heath complex, Allardyce's injury worries look to be subsiding.
But he will still be without defensive trio James Collins, Winston Reid and James Tomkins against Forest with Ricardo Vaz Te and Mark Noble also injured and captain Kevin Nolan banned.
With those key players absent, and a Capital One Cup semi-final first leg against Manchester City just three days later, Allardyce will turn to his Under-21 players for the trip to the East Midlands on Sunday and he is hoping they will see it as a chance to impress on a bigger stage.
"At the moment, my senior squad comprises about 14 fit players, so that's why all the Under-21s will be promoted up into the squad of 25 to face these next group of fixtures," he said.
"The younger professionals will be tested. They were all tested in the summer when we took them away [on pre-season] and we've got to make the squad up with at least seven or eight Under-21 players, who will get the opportunity to play against Nottingham Forest and show us what I can do. We'll ask them 'Are you good enough to play for West Ham?'.
"We all know there is a big jump between there and the first team. Most of them we have tried to put out on loan at first-team level somewhere and now these lads will get a chance alongside a number of experienced players on Sunday."