The Sunderland manager admits that he does not think any of the three struggling sides will be safe before the start of play on the final day.
Barring a minor miracle which could see Crystal Palace go down, only one of Sunderland, Newcastle United, and Norwich City will survive the drop this season.
It is currently the Magpies who look to be in the driving seat at a glance, but Allardyce's side still have fate in their own hands as they sit a point ahead of the Canaries and just a point behind Newcastle with a game in hand over the latter.
The spare match will be played in the middle of next week, meaning that Sunderland could be mathematically safe if they can record back-to-back victories over Chelsea and Everton whilst Newcastle lose away at already-relegated Aston Villa this weekend.
However, though Allardyce is hoping that his players can pull off those results, he acknowledged that realistically he thinks that the fate of all three sides will still be in the balance come 15 May.
When asked if he thought the battle would go down to the final day for all three teams, Allardyce replied, as shown by ITV Sport: "Absolutely, yes. I hope I'm wrong and that we win the next two on the trot because that might be enough, but my gut feeling says it will.
"I hope the players are going to prove me wrong and win the next two on the trot and then see if that's good enough or not, because it may well be that if we beat Chelsea and then beat Everton that we're ok."
Sunderland have pulled off remarkable escapes before in recent years by securing results against big clubs in the final weeks of the season, and they will need to repeat the trick over the next 10 days.