The Baggies appointed Allardyce as their manager in December and he has recently guided his side to only three defeats in their last 10 matches, but they remain 11 points adrift from Premier League safety with five games to play.
Allardyce's Premier League managerial record is impressive when it comes to keeping teams in the division despite all the odds usually being stacked against them, and he is yet to be relegated from the league in his career.
Discussing his future at West Brom, Allardyce told reporters: "That is a discussion that cannot be done at this moment in time. It can only be done when our fate is sealed. If that's what the club wants to do and that's what I want to do, then there are certain criteria that we both have to meet, as there were when I joined.
"I don't think there will be any hesitation from both of us in sitting down for a couple of hours and ripping right through where we are and what we need to do, if we're in the Premier League or the Championship, and then find out which is the way forward.
"My job at the moment is to stay at West Brom and try to keep them in the Premier League. We have tried our best and now we're in a position where I don't think we can afford to lose any game from now until the end of the season."
When asked about his spotless relegation record in the Premier League, the 66-year-old claimed that he would be more upset for the club than himself.
"We have given our all to get the players to maintain our Premier League status. We might fall short but it hasn't been for the want of trying. I would be disappointed to lose my record of always having kept a club up even though I have gone in under difficult circumstances, but we keep going," he added.
West Brom drew 1-1 with Wolverhampton Wanderers in the Black Country derby on Monday night, further harming their chances of Premier League survival. body check tags ::