The Hammers were selected as the preferred tenant of the East London venue by the Olympic Park Legacy Company beating a rival bid from Tottenham.
The Premier League then confirmed that the use of the facility by Spurs or West Ham would comply with their rules, a decision that Orient dispute.
A statement on the club's official website read: "The Premier League rules state that they will not sanction a move unless satisfied that the move will have no adverse effect on another club in the vicinity (The Premier League has accepted in writing that Brisbane Road is in the immediate vicinity of the Olympic Stadium).
"It remains that the Premier League has failed to consider the detriment that would be suffered by Leyton Orient if West Ham United move to the Olympic Stadium.
"All legal avenues are currently being explored."
Source: PA
Source: PA