West Ham have won the battle for the 2012 stadium, BBC London has learned.
Olympic Park Legacy Company (OPLC) executives have decided the offer from the club is a better solution than the rival bid from Tottenham.
The OPLC board will be asked to support the view at a meeting on Friday, when it is expected to confirm West Ham as its preferred bidder.
The government and London's mayor, Boris Johnson, will then take a final decision in the coming weeks.
It would be a surprise if ministers and the mayor overturn OPLC executives, who have spent the last few months discussing the various plans with both clubs in detail.
West Ham are happy for the athletics track to be kept in the stadium and for the venue to be used for a variety of sports and concerts.
Tottenham's plans were to dismantle the stadium in Stratford and build a new football ground in its place.
The Spurs proposal has faced huge criticism from the athletics world, MPs and the public.
A recent BBC London poll suggested 81% of Londoners were against the proposals to rip up the athletics track.
The ComRes phone poll, carried out between 21 and 23 January, also suggested 72% of people in London wanted West Ham to get the stadium, with only 13% supporting Tottenham.
Ministers and the mayor are understood to be well aware that the Tottenham option would have been a "hard sell" to taxpayers