Barry Hearn said the news had emerged from a meeting he had had with the London Legacy Development Corporation (LLDC).
West Ham won the bid to be the anchor tenants but Hearn said the LLDC had confirmed the Premier League club could not block other companies or clubs agreeing deals to use the Olympic Stadium when it was not being used by the Hammers.
Hearn told Press Association Sport: "West Ham have no say about it, that was the most important thing that came out of the meeting.
"I was not sure if West Ham were guaranteed to be the only football club using the stadium and the breakthrough news for me was that the answer is no, they are just a tenant.
"It is a little light at the end of the tunnel, at least we know there are no legal restrictions to us playing there and the next step is to see what the price would be and then make a decision."
Hearn said it would be straightforward to arrange Orient's fixtures around West Ham's matches, or if the stadium was being used for concerts.
The LLDC confirmed that once a stadium operator is appointed anyone, including Orient, can approach them and agree a separate deal - West Ham's matches would have priority however.
An LLDC spokesperson said: "We will be appointing an organisation next autumn to manage, maintain and operate the Stadium and programme activities and events.
"Once they are appointed Leyton Orient are free, as are anyone, to approach the operator to discuss using the Stadium. If long-term use is proposed this would be subject to a further competitive process."