Lue hasn't yet accepted the job, but the two sides continue to work toward a deal.
Although changes can always take place before a contract is signed, this move has been expected, based on the latest rumors coming out of the organization.
Adrian Wojnarowski and Ramona Shelburne of ESPN reported Friday that the Lakers were expected to offer Lue a deal in the coming days.
Lue also had a Lakers-themed birthday cake during his Las Vegas celebration this weekend:
If he does eventually take the job, the 42-year-old would reunite with LeBron James after the two spent parts of three seasons together for the Cleveland Cavaliers. During that stretch, the team went to three NBA finals and won a championship in 2016.
Overall, Lue had a 128-83 regular-season record with the Cavs before he was fired this season after an 0-6 start.
He has also been an assistant with three different organizations and played for seven different teams during his 11-year career. That includes three seasons with the Lakers at the start of his career.
If he takes the job, Lue would be expected to lead Los Angeles back to contention after six straight finishes outside the playoffs.