The Hammers are currently seven points shy of that target with nine games left to play in the campaign.
Allardyce also believes that clubs in the bottom half of the table are all in danger of getting relegated, with Sunderland, Cardiff City and Fulham currently occupying the last three spots.
"I think probably about 38 points [will be enough]," Sky Sports News quotes Allardyce as saying. "Then again, with nine games to go, some have 10, it's swings and roundabouts more than ever before.
"Normally at this stage of the season it's usually down to five or six teams rather than 10. There's still 10 teams, maybe nine now because I think Stoke will be safe.
"Any of those nine need to pick up as many points as they can. Our aim is always to obtain more points than games played, that has been the case since the start of the season."
West Ham will take on seventh-placed Manchester United at Upton Park this Saturday.