The plea, from the npower League One side’s board of directors, adds that the decision ‘could be the death of one of football's most-established community clubs’ with Orient’s Brisbane Road ground within just a mile of the 2012 stadium.
The statement on the club’s official site said: "The decision of the Olympic Park Legacy Company to award the use of the London 2012 Olympic Stadium in legacy to either West Ham United or Tottenham Hotspur will have grave implications on the future of London's second-oldest Football League club and threaten our proud traditions as a community-based club.
"The impact on Leyton Orient will be huge. The prospect of excess capacity leading to discounted tickets and the broader appeal to floating fans of a more high-profile club threatens to swamp us.
"It is tragic to think that the true legacy of the 2012 Olympic Games could be the death of one of football's most-established community clubs. Is that something those in the corridors of power are prepared to shoulder the responsibility for?"
The club also questioned both the Premier League and Football League who they believe would be breaking their own rules if they allowed the move to go ahead.
"The club has appealed to the Premier League and the Football League, both of whom would be in breach of their own regulations if they were to sanction a move for either West Ham United or Tottenham Hotspur, but the silence is deafening," the statement read.
"They both have a regulation which states their boards shall only grant consent to a member club to move to another ground which 'would not adversely affect clubs having their registered grounds in the immediate vicinity of the proposed location'. Surely their boards will recognise this at their respective meetings when the application to move ground comes in from either West Ham United or Tottenham Hotspur?"
Orient has been situated at Brisbane Road since 1937.