"That's not going to happen," Johnson said on First Take.
Johnson also said that the Lakers haven't "event talked about" the possibility of trading the four-time NBA MVP. James, 34, joined the Lakers by signing a four-year contract before the 2018 season.
Johnson resigned from his role as president of basketball operations on April 9. He assumed the role in 2017. The Lakers haven't made the playoffs since the 2012-2013 season.
"This guy is special. [James] has helped our young players so much," Johnson said. "He has made Kyle Kuzma better, Brandon Ingram better. The way he approaches the game and practices, every player now is like 'wow, I've got to get better.'"
Johnson also said James made a large impact and been a "great influence" on Lonzo Ball.
"It's more than just on the court, it's also how to be a professional and also how to take your game to the next level," Johnson said. "And that's why LeBron isn't going..."
"LeBron wants to be the man responsible for leading the Lakers to their next championship."
Johnson said James will be the franchise's "No. 1 recruiter this summer." The former Lakers executive and Hall of Fame point guard did not rule out Toronto Raptors star Kawhi Leonard or Boston Celtics guard Kyrie Irving landing with the franchise.