Midfielder Kevin Nolan is the London club's top scorer this campaign with just six, while their other first-choice strikers have contributed just 10 goals between them in all competitions.
Andy Carroll was supposed to be the answer to their goalscoring woes but he has been hampered by injury since joining from Liverpool on loan last August, notching just three times in 18 appearances.
Despite their out-of-form frontmen the Hammers have managed to keep themselves in the relative safety of mid-table, though Allardyce is taking nothing for granted in the run-in.
Speaking ahead of his team's home clash with West Brom on Saturday, where a win could put them nine points clear of the drop zone, the former Bolton and Newcastle boss concedes he needs to solve his striking conundrum sooner rather than later.
"The only thing I have been disappointed about is our goal tally, particularly away from home," said the 58-year-old. "If we want to be an established Premier League side we've got to have at least a couple of our front men notching 10 a piece, then the rest can follow on behind that."
One player who has been linked with a move to Upton Park is Vitesse Arnhem striker Wilfried Bony.
The 24-year-old has scored 26 goals in the Eredivisie this season and Allardyce refused to rule out a move for the Ivory Coast star - but only if they stay up.
"If we stay in this league every striker is of interest to us if we think they can score goals," he added.