"Several parties" have made approaches and are involved in "an ongoing dialogue" about the possibility of buying the Hammers, according to a senior board member, but negotiations are still at a fairly early stage.
The club, who are currently second from bottom of the Premier League, have struggled financially since the Icelandic economy was hit particularly hard by the recession.
Gold and Sullivan bought Birmingham 16 years ago for £1 and sold the club to Hong Kong billionaire Carson Yeung this October for a price of £82m.
The duo have strong links with West Ham, having once owned a 30% stake in the club.
Sullivan lives in Essex and Gold grew up opposite the Hammers' Upton Park ground, representing the club at youth team level.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.