The Czech Republic international has been a key player for the Hammers ever since his arrival in January 2020, the 27-year-old having contributed 18 goals in 86 Premier League appearances.
With two years remaining on his contract, West Ham will not feel forced to cash in on the player, regardless of whether fresh terms are penned in the future.
However, according to The Guardian, the relevant parties have reached an impasse over a new deal, the top-flight club seemingly not meeting the demands of Soucek's representatives.
West Ham are already in need of signing two new midfielders this summer due to Mark Noble's retirement and Alex Kral returning to Spartak Moscow.
Soucek made 43 starts in the Premier League and Europa League this season, the majority of them alongside Declan Rice.