Co-chairman David Gold has assured West Ham fans the club are working hard to bring in new players and have “many irons in the fire”.
David Sullivan, also a co-chairman, revealed in May the club were prepared to spend up to £30m on a "top striker" as manager Slaven Bilic looks to build on last season's seventh-place finish in the Premier League.
However, the Hammers have been frustrated in their efforts to land a big-name forward, though the club have held discussions with AC Milan striker Carlos Bacca after activating a £26m release clause in his contract, according to Sky sources.
The biggest transfer deal West Ham have struck this summer was to sell James Tomkins to Crystal Palace for £10m but Gold has stressed there is still plenty of time for that to change before the transfer window shuts on August 31.
"I can assure all our supporters that we are still working hard behind the scenes to bring new players into the squad and have many irons in the fire," Gold told the club's website.
"There is still a long way to go before the transfer window closes.
"David Sullivan is working relentlessly to push these players over the line and nobody is better than him at getting the best possible deals."
West Ham had bids for Alexandre Lacazette and Callum Wilson turned down, while Sky sources understand the Hammers were also interested in Michy Batshuayi, who joined Chelsea.
Sullivan also admitted the club were priced out of a move for Leicester City's Jamie Vardy.
Manuel Lanzini was signed from Al Jazira Club for £9.4m after a successful season-long loan, while teenage striker Toni Martinez joined from Valencia for £2.25m.
The club also added Havard Nordtveit, Sofiane Feghouli, Domingos Quina and Ashley Fletcher on free transfers while Gokhan Tore arrived on loan from Besiktas.
Gold is optimistic about some of the young players pushing for inclusion in Bilic's first-team squad and feels many are capable of making the breakthrough this season.
"We have a number of talented youngsters like Reece Oxford, Reece Burke, Martin Samuelsen, Josh Cullen, Sam Byram, Toni Martinez who are knocking on the first-team door," Gold said.
"I have no doubts that these youngsters could be playing in the first-team this year.
"I genuinely don't think we have ever had a crop of young players in my time here who are knocking on the door like the ones we have now. These are serious young talented players."