Allardyce hints at big-name Hammers signing
Enner Valencia, Cheikhou Kouyate and Aaron Cresswell have all made the move to Upton Park in recent months as Allardyce looks to improve on last term's 13th-placed Premier League finish.
And another significant signing could be pushed through ahead of next week's deadline according to Allardyce.
Andy Carroll's persistent injury struggles mean Allardyce could do with another forward and the manager said on Thursday: "We have the budget for one quality player and that's a possibility before the window shuts.
"I think that one more player in the squad and we'd have a good squad this year. Hopefully that's a very fit squad and a squad that produces results.
"I can't see anyone going the other way at the moment [though].
"Then we have an international window and that's good for us with the injury list. Hopefully some of the injured players recover for when we play Hull City [later this month]."
Despite the early stage of the Premier League season, West Ham have been beset with a number of injury problems.
Carroll's ankle problem could see him sidelined until the end of November and skipper Kevin Nolan will miss at least a month with a shoulder injury.
Matt Jarvis (thigh), Carl Jenkinson (hamstring) and James Collins (suspension) are also unavailable for Saturday's home clash against Southampton and Allardyce revealed that striker Diafra Sakho is in doubt with a back problem.
"Sakho tweaked his back on Tuesday too so we're not sure if he'll be fit for Saturday," he added.
"You don't want to be faced with that many injuries, but we're looking pretty good with the way we're playing."