The 24-year-old is undergoing a medical at the club's Rush Green training ground.
Speaking about Soucek, boss David Moyes said: "I'm hoping that he's in the middle of his medical just now. I think he gives us a lot of different aspects but more importantly he fits the profile of the player I want to bring to West Ham.
"I said I want to bring young players but we also need experience too and I think at the moment, he helps with both of those.
"He's captain of Slavia Prague, he's played defensive midfield but scored a lot of goals as an attacking midfielder too.
"We needed a bit of it all, some cover, another midfield player, obviously goals, so at the moment he ticks a lot of boxes."
Moyes also confirmed a bid is in for another player, with reports linking the club with RB Salzburg right-back Rasmus Kristensen.
West Ham are desperate to strengthen their squad before Friday's deadline, especially after the club's financial report on Tuesday morning came with a warning of the dire consequences of relegation.
The Hammers made a pre-tax loss of £28.2million for the last financial year, and joint-owner David Sullivan insisted staying in the Premier League was "an absolute necessity for the future wellbeing of the club".
West Ham currently lie above the relegation zone on goal difference, and a heavy defeat by leaders Liverpool on Wednesday night would see them slip into it.
But Moyes remains confident he can guide them away from trouble for the second time in three seasons.
"There are parallels to my last spell here," he added. "We've quite a similar points tally, we have been here before and done it before, some of the players too – but we need to pick up points, we are not kidding ourselves.
"There are a lot of teams scrapping it out but I do believe we can do it. If we can add to the squad a little bit then hopefully it'll help."
Goalkeeper Lukasz Fabianski and midfielder Robert Snodgrass could be fit to face Jurgen Klopp's side after missing Saturday's FA Cup defeat by West Brom through injury.