He has increased both his scoring average and field goal percentage in each of the last three seasons, coming in at 16.1 a night on 55.8 per cent from the floor last season in 82 games for the Lakers.
National Basketball Association insider Adrian Wojnarowski first reported the news.
Cousins was in line for a max deal last season until he tore his achilles tendon while playing for the New Orleans Pelicans.
Rondo reportedly agreed to sign a one-year contract with the Lakers on Monday.
The floodgates have opened for the Los Angeles Lakers as the news of LeBron James' signing has kicked off a flurry of moves. Unless Ball is traded away, he would most likely be demoted to a bench role with fellow youngsters Josh Hart and Moe Wagner.
LeBron James' decision to join the Lakers marked an excellent start to Magic Johnson's plan to turn Los Angeles into a contender. He also played for the Celtics when the Lakers won the 2009-10 championship over Boston in seven. The Lakers did not reach the playoffs during his four seasons.
Deng's $36 million salary would then be paid out over five seasons.
Randle, 23, was originally drafted by the Lakers with the seventh overall pick of the 2014 draft. The next big question revolves around free agent DeMarcus Cousins.
He has career averages of 13.5 points and 8.9 rebounds in 238 National Basketball Association games (182 starts).