Allardyce wants another striker for West Ham
Allardyce has added full-backs Carl Jenkinson and Aaron Cresswell to his squad since the end of last season, while Cheikh Kouyate and Diego Poyet have increased his midfield options.
Forwards Enner Valencia and Mauro Zarate have also joined the London club, but another injury blow for Andy Carroll has prompted Allardyce to scour the market for another forward.
Hugo Almeida, Joel Campbell and Samuel Eto'o have all been linked with a switch to Upton Park and Allardyce has informed co-owners David Gold and David Sullivan that he needs additional firepower to round off his transfer dealings.
"I think from a defensive point of view, we've finally finished our recruitment for this season," he told the club's official website.
"I think we now have Joey O'Brien and Aaron who can both play at left-back. Joey has filled in at left-back several times and he does just as good a job there as he does at right-back.
"That means that Carl can come in and compete with Guy Demel, so we're comfortable in the right-back position now.
"Of course we hope our central defensive threesome of Ginge (James Collins), James Tomkins and Winston Reid stays fit all season, and we've got two good goalkeepers so we're defensively fine.
"Midfield, moving forward we have brought in Cheikh and he'll have to integrate to the Premier League, which is not easy when you first arrive here, so we have to keep an eye on that.
"Diego has settled into the first-team squad quite well. I'm not saying he is going to play 20 or 30 games, but hopefully he'll play some part this year in the Premier League.
"Then of course Enner has got into the country and has brought his partner with him. That process of giving him a pre-season starts now.
"Mauro has fitted in reasonably well, but he's had a little injury and has had slight issues with his match-fitness, but he's here.
"We still have one more to go in the recruitment process and I've been speaking to the joint chairmen this week.
"Hopefully that player will bring something in terms of our capability of scoring more goals - not creating, because we've always been able to create."