Allardyce appears to have steered the Hammers clear of relegation danger in recent games, with the club sitting 12th in the table on 37 points after frustrating Liverpool in a goalless draw at Anfield on Sunday.
The manager has previously cited 38 points as the safety barrier but feels it might take 40 to ensure the Hammers' survival this season, with only six points currently between themselves and third-bottom Wigan.
He hopes West Ham can hit that target sooner rather than later as they prepare to take on Southampton at St Mary's stadium this weekend.
He told Sky Sports: "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.
"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."
Allardyce says he is delighted to see West Ham where they are in the table after securing promotion from the Championship last season.
Asked if he would have taken their current position at the beginning of the season, he added: "I'd have snatched their hands off. 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 in talks with Allardyce over a new contract, with his current deal set to expire at the end of the season.
The manager and the club's owners have previously said an extension will only be agreed once Premier League safety has been secured.
West Ham defender James Collins, who re-joined his old club last summer from Aston Villa, hopes Allardyce will commit to the Hammers sooner rather than later.
The Welshman 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."