Manager Allardyce's future has been up in the air since the turn of the year, with owners David Sullivan and David Gold keen to make sure that the club's Premier League status was secure before extending the contract of the man who got West Ham promoted last season.
Speculation has mounted in recent weeks that the Hammers have been considering appointing a new boss, such as club icon Paolo Di Canio, at the end of the season, but Allardyce revealed earlier this week that he has agreed the framework of a new deal.
Allardyce will not sign the contract until his team arrive at the points haul he thinks will guarantee West Ham's Barclays Premier League status.
"I always want to know we are safe first (before signing)," Allardyce said.
"I suppose I could sign a contract that said if we get relegated then I don't want it, but I won't do that.
"We think we will be safe at 38 points. Then we can push on to 40 if we can.
"The contract negotiations are ongoing at this moment in time. We talk confidentially among ourselves and hopefully we can come to an agreement shortly."