The Hammers have a long-standing interest in the Algerian striker and have been talking to Inter since December.
The player, who is co-owned by Parma, is now due to arrive in England to undergo a medical ahead of a loan move, with a view to a permanent deal in the summer.
The fact West Ham had to negotiate with both Inter and Parma was the main reason they have taken longer than they had hoped to push through a move.
Now Belfodil is expected to sign ahead of this weekend's clash with Cardiff City, and Allardyce admitted after a heavy defeat to Manchester City in the League Cup on Wednesday night that he is closing on the addition of fresh faces.
"We are trying very, very hard and we are trying to clinch a couple of deals," he told Sky Sports.
Belfodil only joined Inter from Parma in the summer but has found first-team football hard to come by and, with the World Cup in mind, he is anxious to see more playing time.
Giant Monaco striker Lacina Traore could also be on his way to help bolster Allardyce's squad but faces a work permit hearing on Monday before he is able to seal any loan move.
Portugal striker Hugo Almeida - currently with Besiktas - is another centre forward understood to be on the club's radar.