Leyton Orient have applied for permission to move to the Olympic Stadium in east London after the 2012 Games, with the club's chairman Barry Hearn calling for West Ham to be ruled out of the running under Football League rules.
Hearn said last week that his club would be interested in becoming tenants at the Stratford site after the Olympic Park Legacy Company reopened the tender process to rent the stadium.
A deal with West Ham and Newham Council collapsed amid legal challenges, with the Government announcing last week that the stadium would remain in public ownership and be leased out.
Hearn believes the application to the Football League is significant, arguing that they would not sanction another member club - West Ham - moving closer to Orient's home if it affected their business.
Hearn told his club's official website: "We are asking for a 25,000-seat stadium and we want to see if we can get around the athletics track. It has to stay, we know that. But can we build up, if not down, and see if it's possible to get it covered while we play?
"If it isn't possible, it isn't - and we wouldn't move in with a running track between the pitch and the crowd.
"We have submitted an application for permission to move to the Football League, and that permission is something that West Ham don't yet have.
"It was the Premier League who gave them the green light to move in their original plan, but they are no longer members of the Premier League.
"The rules are that the Football League would not sanction a club moving closer to another club if it affects the business of that other club, and there's no doubt that West Ham moving there would affect us.
"West Ham can't just assume that they will be in the Premier League by then. How, therefore, can the Olympic Park Legacy Company, whose job it is to decide who takes over the stadium, allow West Ham to remain in the bidding process? We want them thrown out because they don't have permission from the relevant authority - the Football League."