A judicial review is being held at the High Court on Thursday to look into the decision by the London Legacy Development Corporation (LLDC) to award sole tenancy to the Hammers, who will move into the site in 2016.
A decision is not expected for a couple of weeks and Leyton Orient chairman Hearn believes his club has a good chance of winning.
Hearn said: "I am looking for a ground-share, I don't want compensation. Compensation gets spent - I am looking for the future and a ground-share at the Olympic Stadium which makes sense from the taxpayers' point of view.
"They have spent £600million of taxpayers' money on the stadium and they must have full use for that money and I think Leyton Orient can make a meaningful contribution to the financial burden of that stadium.
"We hope the outcome of the judicial review will mean Leyton Orient having the opportunity, which they should have had before, to meaningfully discuss a ground-share arrangement with West Ham."
Hearn claims the LLDC did not follow bidding rules properly when it accorded the stadium to West Ham.
He added: "The review can say that they believe the bidding process was not carried out in accordance with the rules and this stopped us having the discussion on ground-sharing we wanted to have.
"We are asking for that process to be re-opened and full disclosure of all the dealings between West Ham and LLDC.
"I think it's 50-50, my lawyers are hopeful we are going to win.
"The reason we want full disclosure is we think LLDC have come to an arrangement with West Ham which is not in line with the bidding process rules."