talkSPORT understands the Hammers are targeting two more signings as the deadline approaches on September 1.
On Wednesday, they confirmed the signing of Germany international defender Thilo Kehrer from Paris Saint-Germain in a £10.1million deal.
It follows the additions of striker Gianluca Scamacca, centre-back Nayef Aguerd, winger Maxwel Cornet and midfielder Flynn Downes.
David Moyes wants another midfielder and a left-back before the window closes.
"West Ham are going to be busy in the next couple of weeks," talkSPORT's football correspondent Alex Crook said. "The owners are committed this summer to trying to give David Moyes all the resources to have another tilt at European football.
"We know they are interested in Hans Vanaken, a central midfielder currently playing for Club Brugge in Belgium.
"Their initial of €10m (£8.4m) was rejected, my understanding is they are preparing to up that bid.
"He is a tall central midfielder, athletic, and a typical David Moyes signing.
"West Ham are hopeful, having missed out on Emerson at Chelsea due to his wage demands, they can get this deal done.
"They are still looking at a potential left-back as well. West Ham's business is far from done."