West Ham vice-chairman Karren Brady believes the club would be the “best anchor tenant” for the stadium post 2012.
The Hammers’ plans include sharing the stadium with Essex Cricket Club and staging athletics, rugby and entertainment events at the Stratford site.
Brady estimated the conversion costs at between £150m and £180m to extend the roof, create a pitch, turnstiles, toilets and space for corporate hospitality.
She said the club plans to raise the money by making use of the extra space and offering the stadium for other events when it is not in use for football.
West Ham want to transform the 80,000 seat Olympic Stadium into a 60,000 seater football ground.
Rival legacy plans involve dropping the capacity to 25,000 to form a permanent athletics venue.
One source close to the site told the Enquirer: “The conversion costs are huge whatever the use so it makes sense to go with West Ham who are the biggest club in the area.
“Demand for football will always be higher than athletics and with West Ham you get a guaranteed crowd with the stadium in regular use on match days plus the club’s plans for other events at other times.”
Brady said: “We have made no secret of the fact that we believe that we would be the best anchor tenant and provide the best usage for a stadium of that size where we can not only incorporate Premier League football, we can add athletics, we are doing our own discussions with international cricket and of course with rugby as well, truly making it multi-purpose.”