As confirmed by his agent, Jared Karnes, Beasley has met twice with the Lakers this off-season but has yet to reach any agreement with the team on a contract.
Prior to trading Derek Fisher for Jordan Hill in 2012, the Lakers were close to acquiring Beasley from the Minnesota Timberwolves. Though Beasley is a gifted scorer, he has yet to find a long-term home in the league.
According to USA Today, the Lakers also worked out seven other players Tuesday, including centers Dexter Pittman, Greg Stiemsma and Daniel Orton, and guards Bobby Brown, Ben Hansbrough, Toney Douglas and Malcolm Lee.
Stiemsma was waived after 55 appearances with the New Orleans Pelicans, after struggling with knee injuries. Through three seasons, the 6-11 center has averaged 3.4 points and 3.6 rebounds with the Boston Celtics, Timberwolves and Pelicans.
Orton, at 6-10, has yet to find his place in the NBA, playing 51 games with the Orlando Magic, Oklahoma City Thunder and Philadelphia 76ers since 2011 -- averaging 2.8 points and 2.5 rebounds.
The Lakers may be looking to bring on an additional point guard, given Steve Nash's struggles to stay healthy (back, knee and hamstring).
Both Brown and Douglas are contracted to play overseas in China, although they may be able to get out of their deals to join the NBA. The Lakers originally drafted Douglas for the New York Knicks in 2009 (29th overall pick).
Douglas was traded midseason from the Golden State Warriors to the Miami Heat, advancing with Beasley to the NBA Finals in a losing effort against the San Antonio Spurs. Through 27 games with Miami, Douglas averaged 4.2 points and 1.8 assists.
Brown has logged 113 games in the NBA with the Sacramento Kings, New Orleans Hornets (now Pelicans), Timberwolves and Clippers. The 29-year-old combination guard has had greater success in China and Italy.
Hansbrough played one season with the Indiana Pacers, averaging 2.0 points and 0.8 assists through 28 games.
Lee, the lone shooting guard in the workout, spent two seasons with the Timberwolves (2011-13), averaging 4.0 points while shooting 38.5%.
The Lakers currently have 13 players on their roster, but can bring as many as 20 to training camp. The maximum for the regular season is 15, giving two free agents a chance to stick with the team into the year.
The most the Lakers can offer any free agent is a minimum contract, starting at $507,000 for a rookie while ramping up to $1.4 million for players with at least 10 years in the league.