Allardyce has already been busy since the end of last season, bringing in forward Mauro Zarate, left-back Aaron Cresswell and midfield duo Cheikhou Kouyate and Diego Poyet.
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"I think there are three or four positions - it depends on the budget," Allardyce told the club's official website. "You would say there is still room for a young central defender.
"You would also say we need another left-back to go along with Aaron and I think a front-line player and the possibility of a midfield player as well."
Poyet, 19, completed his switch to Upton Park from Championship outfit Charlton Athletic on Tuesday.
Allardyce is planning on using the youngster during pre-season, but admitted his competitive debut is likely to come when West Ham enter the Capital One Cup.
"Like all the young players, we'll try him out in the pre-season," he added. "We may try him out, if he progresses well, in the early stages of the Capital One Cup if the opposition are from a lower division than ourselves.
"That system progressed us to a fantastic run last season to the semi-finals and we nearly made Wembley."
Meanwhile, West Ham freed up space in their squad by releasing midfielder Alou Diarra on Wednesday.
The 32-year-old made just six league appearances for the club after joining in August 2012.
"West Ham United and Alou Diarra have reached a mutual agreement to terminate the midfielder's contract with immediate effect," West Ham posted on their official Twitter account.