The Czech Republic international has been given permission by Slavia Prague to travel to London for a medical.
West Ham hope to wrap up a deal to make the 6ft 4ins defensive midfielder their second signing of the month.
Soucek has 23 caps for the Czech Republic and has been identified by David Moyes and his top target to add some steel to the Hammers squad.
The 24-year-old has yet to agree personal terms with West Ham but a deal is close.
Moyes has targeted a midfield player to ease the burden on captain Mark Noble.
West Ham co-owner David Sullivan wants to bring in at least two players before Friday’s transfer deadline to deflect some of the growing discontent among the club’s fans.
The club also want to sign a full-back and have enquired about Nottingham Forest right-back Matty Cash.