Both Premier League club have submitted bids to the Olympic Park Legacy Company (OPLC) which is holding a board meeting on Friday to confirm West Ham as its preferred choice, the unsourced report on the BBC's website said.
Should West Ham, whose plan would retain an athletics track in the stadium, be confirmed as the OPLC's preferred tenants it would still need to be ratified by the government and London's mayor Boris Johnson.
Tottenham's plan has attracted criticism because the north London club were going to demolish most of the 500 million pounds stadium and replace it with a 60,000-seat purpose-built football stadium.
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The OPLC were unavailable for comment on Wednesday while a spokesman for London's Olympic organising committee (LOCOG) said they had not been informed of any decision on the stadium.
