The Hammers moved six points clear of the relegation zone following Sunday's 0-0 draw with Liverpool at Anfield, but the 58-year-old is not ready to relax just yet
The Hammers currently sit in 12th place in the top flight following Sunday's 0-0 draw with Liverpool at Anfield having moved onto 37 points with seven games remaining.
However, the Englishman insists it is vital that the east London club assure their safety by earning another three points.
He told reporters: "We may [have to] sneak the points total up maybe one or two more, but I certainly think 40 now is definitely going to be good enough.
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"Wigan have put a run together, Southampton have put a run together, Aston Villa have done it. I thought probably 38 but if you're going to be absolutely [sure], we're going to still go to the golden 40 aren't we."
The 58-year-old went on to admit, however, that he would have taken his side's current position if offered it at the start of the season.
"I'd have snatched their hands off," he added. "In fact I probably would have gone further than that, I would have cut their hands off, if that's the right terminology."
West Ham are currently in discussions with Allardyce over a new contract, and defender James Collins has voiced his eagerness for the former Bolton boss to commit his future.
He said: "He's been great. He's been one of the main reasons I came back, to work with the gaffer.
"Everyone obviously speaks very highly of him and he showed it again, his tactics at Anfield were spot on and they have been all season. So fingers crossed that he can get the contract sorted."