The Alouettes play Saturday in Calgary, and coach Tom Higgins says the defensive end could compete in any of the five games in August.
Higgins says Tuesday that Sam is "is getting so much closer to being able to play. He wants to go, and I think it's going to happen sooner than later."
Sam wasn't made available for comment.
Sam became the first openly gay player drafted by an NFL team when the St. Louis Rams picked him in 2014. He didn't make an NFL roster and recently signed a two-year contract with Montreal in the Canadian Football League.
Sam left two weeks into training camp to attend to personal issues, returned on June 29 and has been getting into shape.