Sources told TMZ Sports it's "not a done deal," but another said that "all signs point" to the 13-year-old playing his high school ball in L.A.
The report will further fuel speculation that the elder James plans to sign with the Los Angeles Lakers this offseason.
Among the players currently attending Sierra Canyon are Kenyon Martin's son, Scottie Pippen's son and Derek Fisher's nephew.
Additionally, Sierra Canyon is "holding a place" for Bronny whenever he makes his high school decision, per TMZ Sports.
Last week, OddsShark tweeted that the Lakers are the heavy favorites to sign James this offseason at 4-13. The next closest team on the list is the Cleveland Cavaliers at 13-4.
LeBron has until Friday to decide whether to opt in to the final year of his contract and remain with the Cavs or opt out and become a free agent.
James has led the Cavaliers to four consecutive NBA Finals, but his supporting cast left plenty to be desired last season following the trade of guard Kyrie Irving to the Boston Celtics.
If LeBron signs with the Lakers, the potential is present for another superteam.
Paul George could possibly join him since L.A. has the room to sign two big-time free agents. The Lakers could also attempt to pry Kawhi Leonard away from the San Antonio Spurs via trade.
Additionally, the Lakers boast some impressive young talent in the form of Brandon Ingram, Kyle Kuzma and Lonzo Ball.
James' decision doesn't necessarily have to be tied to what his son does, but if Bronny goes from Ohio to L.A., there will inevitably be talk that his father will do the same.