ESPN and The Los Angeles Times reported the Lakers are expected to trade forward Brandon Ingram, point guard Lonzo Ball and shooting guard Josh Hart for Davis, who requested a trade earlier this year.
The trade cannot be made official until July 6.
The Pelicans also will receive three first-round picks, including the No. 4 overall pick in Thursday's NBA Draft. New Orleans also has the draft's No. 1 overall pick, which is expected to be used on Duke forward Zion Williamson.
Davis was the No. 1 overall pick in 2012. He is a six-time All-Star who averaged 25.9 points, 12 rebounds, 3.9 assists and 2.4 blocked shots in 56 games last year.
The trade pairs Lakers forward LeBron James with a second superstar. James missed the NBA Finals for the first time since 2010 this season.
Los Angeles previously tried acquiring Davis before the Feb. 7 trade deadline. The Lakes are also expected to pursue Charlotte Hornets point guard Kemba Walker in free agency, The New York Times reported.
The Lakers went 37-45 last season and have not made the playoffs since the 2012-13 campaign.