Some West Ham supporters unveiled a banner saying "Fat Sam Out - Killing WHU" during Saturday's 1-0 defeat at West Bromwich Albion that left them in 14th on 37 points, five clear of the relegation places.
West Ham face a tough task to halt the slide with final fixtures at home to Tottenham Hotspur and away to Manchester City, with the club's owners wanting points in the final two games.
"We've had preliminary discussions but all of those have been on hold for the last four games," Allardyce was quoted as saying by the British media on Monday when asked if he had the backing of the board.
"We were on 37 points and we all said: 'Just pick up another couple and we can really look to plan for next season'."
The former Blackburn Rovers boss has struggled to win over his West Ham detractors in the three years he has spent with the club despite gaining them promotion back to the Premier League and being on the verge of keeping them there once again.
He has one year remaining on his contract but disgruntled fans have rarely warmed up to his supposed long ball tactics, instead craving more eye-catching, passing methods displayed by West Ham sides of the past.
Allardyce defended his team's style.
"At times we play good football and create chances but when we lose matches on a regular basis it's not acceptable for anybody, never mind me, the fans, the players," he said.
"Performances mean nothing if you don't get results.
"We've got to make sure we turn it around with two games to go. I can hear the chanting, I know about that. The only way to do anything about that is to win football matches. Criticism comes on me because I'm responsible to make the team win.
"My job is about working with the players that I have and about working with the owners to build a better football club than they've had ever before."
West Ham co-chairman David Sullivan was guarded in his view after the increased protests at West Brom.
"I am not saying anything now. We'll discuss it at the end of the season as we always do," he said.
Allardyce admitted things had not gone as well as he planned this season after leading the club to 10th in their first year back in the English top flight.
Injuries have hampered their progress, with a number of defensive ailments leaving them in the relegation zone at the turn of the year, but Allardyce was confidently planning for next season and talking about transfer budgets.
"Overall this season we haven't really been as good as we should have been and we haven't really produced as many results as we should have done. So getting better and improving that is the highest thing on the agenda," he added.
"I'm well aware of the situation in terms of how we have to finish the season off - as high as we possibly can, in terms of performances and results.
"I know there is a huge amount of work to be done in the summer, hopefully for me to make the squad better."
- Sports & Recreation
- West Bromwich Albion