The Hammers have splashed the cash already this summer, bringing in the likes of Angelo Ogbonna, Pedro Obiang and Dimitri Payet.
However, manager Slaven Bilic still needs more reinforcements, and bringing in a winger would give the Croatian tactical flexibility, with few options out wide right now.
The Sun report that the Hammers have been keeping tabs on Midtjylland sensation Pione Sisto, and sent scouts to watch him in action against Southampton on Thursday.
The 20-year-old, born in Uganda, is one of Denmark's hottest prospects having played a starring role with Midtjylland, and interest in his signature is unsurprisingly rising.
With blistering pace and superb trickery, Sisto is an up-and-coming star out wide, and he showed that with an impressive display against Southampton.
It's now reported that West Ham scouts were in attendance to assess Sisto's display, and The Sun report that a £4m offer could be enough to land the Danish Under-21 international, with whom he has scored four goals in four games.
It would be a real coup for West Ham to snap up Sisto, and whilst a deal may not be possible before the deadline, it seems clear that Bilic wants to add some pace out wide to help his attack.