Vardon also reported Friday that James will not pick up the $35.6 million option in his contract with the Cleveland Cavaliers, meaning he will become a free agent.
The Lakers have long been considered a major player for James. Kevin O'Connor of The Ringer reported in March that the Lakers, Cavs, Philadelphia 76ers and Houston Rockets were the teams LeBron would consider joining.
L.A. is now a substantial favorite to land James in betting circles as well. OddsSharktweeted last week that the Lakers are 4-13 favorites, while Cleveland is a distant second choice at 13-4.
The Lakers have created enough cap space to sign two star players in free agency, meaning they could entice James to sign by landing another All-Star such as Paul George, Chris Paul or DeMarcus Cousins.
Also, the Lakers are in talks with the San Antonio Spurs to trade for disgruntled forward Kawhi Leonard, per ESPN's Ramona Shelburne, Adrian Wojnarowski and Brian Windhorst.
Since Leonard's contract will pay him a reasonable $20 million in 2018-19, it is possible that the Lakers could create their own version of the Big Three with LeBron, Kawhi and a third player with George standing out as the most obvious candidate since he is a Palmdale, California, native who has been linked to the Lakers in the past.
LeBron already left the Cavs once to join the Miami Heat, but he returned with the stated goal of bringing a championship to Cleveland.
He accomplished that, and reached four consecutive NBA Finals.
His supporting cast with the Cavaliers failed him often last season, though, and there appear to be far better options on the table.
The Lakers' cap flexibility may put them atop the list, plus James could relish the distinction of bringing arguably the greatest franchise in NBA history back to glory after five straight seasons without making the playoffs.