Sullivan and Gold want to lease the stadium from Newham Council and are keen for the running track to be removed with the capacity being around 55,000.
The Olympic Stadium in Stratford is about three miles from the Boleyn Ground, the official name for West Ham's Upton Park home.
It is a similar arrangement that Manchester City have at their Eastlands Stadium, which was originally built for the failed 2000 Olympic bid and later used for the 2002 Commonwealth Games.
Bonds made over 600 appearances for West Ham
"If we could get this huge ground, we could take football back to the people," Sullivan said. "We could reduce the admission prices to the cheapest in the Premier League because we would have the capacity to do it."
Sullivan and Gold completed their takeover of the debt-ridden club which is valued a £105m on Tuesday. The pair are well used to turning around the fortunes of football clubs having taken over bankrupt Birmingham in 1993 and guided them into the Premier League.
However, supporters complained about season ticket price rises while they were in charge at St Andrew's.
A move to the Olympic venue would require approval from the British Government and the Olympic Park Legacy Company (OPLC), which pledged to adapt the £500m stadium into a venue capable of hosting major athletics events as part of its successful bid to secure the Games.
The OPLC says it is keeping an open mind on future use of the stadium and "not ruling anything in, not ruling anything out".
But Sullivan said he thought there was a better than 50-50 chance of the government agreeing to let West Ham become tenants of the stadium.
The former Birmingham co-owner also suggested it could be cheaper to build a new track and field venue elsewhere, with Upton Park a possible option.
There is also the possibility of keeping the running track but installing retractable seating, similar to that of the Stade de France in Paris, although that would require significant engineering work.
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