The Hammers were formally awarded a 99-year lease on the stadium in March and are due to occupy it from 2016 but a House of Lords report, published on Monday, recommended that the two clubs work together following a lengthy legal dispute from the League One leaders over their hopes to move there.
The report suggested that Orient be allowed occasional use and the smaller side's chairman, Barry Hearn, is keen for three-way discussions between the clubs and the London Legacy Development Corporation (LLDC).
But a West Ham spokesman declared: "Looking forward, our focus is solely on creating a stunning new home for the club and its supporters in 2016, alongside a long-term legacy for the community of east London.
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"We welcome the committee's comments and are happy the House of Lords have recognised that West Ham's selection will ensure the stadium reaches its full legacy potential."
Hearn told the League One team's official website: "I agree with the House of Lords recommendation - ourselves, West Ham and the LLDC should sit down and work this out together once and for all.
"Leyton Orient is a local club which undertakes a huge amount of community work in one of the poorest areas in London.
"It has been said that Orient did not bid enough to cover its costs of using the stadium but we were bidding within our means and against ourselves - we do not know what the LLDC want from us because they will not tell us so we ask them again, publicly, to say what we have to pay to share the stadium, a national asset which is on our doorstep.
"We are writing to the LLDC seeking a meeting so that we can have an open and transparent discussion about what part we can play in the future use of the Olympic Stadium."