With Southampton relegated from the league, three teams - Leeds United (19th), Leicester City (18th) and Everton (17th) - remain in danger.
Leeds have lost seven of their last 10 league games and are second-bottom in the standings with 31 points and a game to go. They need to win the season's final match to have a chance of staying up, but will still need other results to go their way.
"I love the mood and application. We have been training at the ground because here is where we will live or die on Sunday, in terms of the result," Allardyce told reporters ahead of Sunday's game against Tottenham Hotspur at Elland Road.
"All we can try to do is give the players the best opportunity possible to get the result they need.
"It's all about this stadium on Sunday and the fantastic atmosphere that will go with it... I hope we can go one step further and win the game."
The veteran coach, who was brought in at Leeds earlier this month with just four games left, said Scottish greats Eddie Gray, Gary McAllister and Gordon Strachan visited the Leeds players ahead of the high-stakes encounter.
"It's about how important Leeds is and what it meant to them - the history of the football club and the fact they had very successful times here," Allardyce said.
"It's about improving our mentality to deliver. A different voice speaking about what they did at this football club and how much they love the club is really important."
Allardyce said they "will be happy to gamble on anyone's fitness", adding that Rodrigo has trained while fellow forward Patrick Bamford will be assessed.
