The job is open after the Lakers parted ways with Luke Walton at the end of the regular season.
Last Friday, Wojnarowski called Lue the "strong frontrunner" in the Los Angeles coaching search.
Lue was an assistant coach for the Boston Celtics, Los Angeles Clippers and Cavaliers before taking over as the head coach in Cleveland during the 2015-16 campaign after the organization fired David Blatt.
He went on to lead the Cavaliers to their first championship in franchise history, guiding them back from a 3-1 deficit against the 73-win Golden State Warriors in the NBA Finals.
Cleveland reached the NBA Finals in each of Lue's next two years but lost to the Warriors on both occasions. While the Cavaliers fired him following an 0-6 start in the 2018-19 campaign and James' departure, Lue still sported an impressive 128-83 record as the head coach of the Cavaliers.
Lue is familiar with James and found the success in Cleveland that Los Angeles is looking for, but Marc Stein of the New York Times reported people around the league believe "some in the Lakers' organization may fear hiring Lue would be giving LeBron too much control."
The Lakers have not reached the playoffs in any of the last six seasons and were arguably the NBA's biggest disappointment in 2018-19 after finishing 10th in the Western Conference and 11 games out of the playoff spots.