The Hammers had been pursuing the 17-year-old along with Tottenham and Brighton & Hove Albion, however, all three are said to be perturbed by a £1million-plus price hike.
Browne, a central defender, is believed to have spent time with the Irons on trial, suitably impressing during his time in east London.
There is doubt over whether any of the clubs interested will renew the pursuit in the summer given Birmingham’s new demands.
A move for the Birmingham starlet would certainly be in keeping with the desire to sign youth prospects at the club.
Having signed Danish centre-back Frederik Alves in January, the drive to recruit players for the next generation is there for all to see.
Clearly, none of the interested parties wants to be held to ransom on this deal, although the demands aren’t extortionate in the grand scheme of Premier League deals, Birmingham have recently set a precedent for themselves in the deal which saw Calum Scanlon join Liverpool.