The England international has not hit the back of the net in 11 league games, and could mark his longest stretch without a goal if he does not score against Manchester City
The 23-year-old, who is with the Hammers on a season-long loan from Liverpool, has not scored in 11 league games - one shy of a personal record drought.
And, after a hamstring injury disrupted the striker's start to life in London, Allardyce has conceded that the £35 million man simply needs a goal.
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“I don’t think frustration helps you. I think you like to come, start and get off the mark as quickly as you possibly can.
“So we have got to keep providing the service and eventually, he’ll start putting it in the net, we hope.
“The more he plays with our players, the more he can start to read how the situation develops and hopefully get on the end of it.”