The French team swept the podium in the event.
The Canadian Olympic Committee, along with the Slovenian Olympic Committee, are alleging that French team staffers changed the shaping of the athletes' ski pants for better aerodynamics.
The ad hoc division of the Court of Arbitration for Sport is scheduled to hear the case Saturday night.
Leman finished fourth in the final to Jean-Frederic Chapuis, Arnaud Bovolenta and Jonathan Midol of France in Thursday's competition. Slovenia's Filip Flisar placed second in the small final and would be bumped to bronze if the appeal is won. Russia would win the silver.
The Canadians and Slovenians initially requested that the world governing body of skiing disqualify the French competitors. But the FIS competition jury decided the protests couldn't be heard because they weren't filed on time after the race.
A decision by the CAS is expected Sunday.
The Canadian Olympic Committee didn't immediately respond to an email request for comment.
Leman reached Thursday's final after dominating the two previous rounds, but got off to a slow start in the medal round and then fell while trying furiously to catch up.
"I was in disbelief, almost, when I was lying there," he said after the race. "But it's part of skicross."
It was a second Olympics in a row to end in disappointment for Leman. At the Vancouver Games, he didn't get to compete after fracturing a leg during a practice run.
"I just feel slightly better, right now, than I did in Vancouver," he said. "It sucked watching my teammates from the stands, and all I wanted here is a chance.
"I gave myself a really good chance today, and that I'm really proud of that, but it sucks to be so close to the podium."
Leman shrugged off talk he may have been intentionally shut out by the French skiers. He fell too far behind from the start and only briefly had a one-on-one battle with the last of the three leaders.
"No, they were all trying for it, they were going for it," he said. "They skied the same as if it had been three different nations."
"Everyone was trying to pass and that's in part why I ended up getting stuck on the outside. I probably should have tried going inside, but we have to make split-second decisions. You can't get them all (right) over a day of skicross. At some point you run out of luck — like I did a couple of hundred metres short."