Nick Young is doing his best full-court press on LeBron James' son, Bronny -- telling TMZ Sports the basketball phenom should play college ball at USC instead of Ohio State.

The NBA superstar's oldest son had the sports world buzzin' after posing in a Buckeyes uniform this week ... just days after the James gang hit up the OSU-Notre Dame football game on Saturday.

Bronny has made it clear he still hasn't committed anywhere, but he seemed to embrace wearing the Scarlet and Grey ... evidenced by how happy he and his parents were during the photoshoot.