Johnson was released in training camp by the Miami Dolphins two years ago following a domestic dispute with his former wife, Evelyn Lozada. Johnson hasn't played in an NFL game since the 2011 season with the New England Patriots.
"If they did [call], he would jump for it," Rosenhaus told ESPN.com Wednesday at Dolphins camp. "Of course, he would love it. But right now, he's operating as a Canadian Football League player. We will see what happens. It's not like we're holding our breath that he's going to play in the NFL. But he's trying. That's the goal."
Johnson signed a one-year contract with the Alouettes this past April. He currently has four receptions for 78 yards and a touchdown for Montreal (1-4) this season.
Training camp and the preseason are times when injuries often occur in the NFL. But chances appear slim that Johnson would get another call. According to ESPN Stats and Information, Johnson, 36, would be the oldest receiver in the NFL this season. Reggie Wayne, 35, of the Indianapolis Colts currently holds that distinction.
"He would tell you that he could still do it better than anybody," Rosenhaus said of Johnson's age. "He doesn't lack confidence or enthusiasm."
Johnson, in his prime, was once one of the NFL's most prolific receivers. He recorded six consecutive 1,000-yard seasons from 2002-07 as a member of the Cincinnati Bengals. Johnson has 766 career receptions for 11,059 yards and 82 touchdowns in 11 NFL seasons.
Rosenhaus said Johnson is enjoying life in Canada and simply being back on the football field.
"He just loves playing football -- Chad is a guy that will play football until he's 50 if they let him," Rosenhaus explained. "He loves the game. He's really very passionate. He's got to do something with football, it's just his life. It really is. All his Twitter followers are enjoying him in Canada just like they would in the NFL. It's nice to see."