Odom last played for the Los Angeles Clippers during the 2012-13 season, averaging a career-low 4.0 points and 5.9 rebounds. Clippers coach Doc Rivers met with him last month, but apparently nothing came of those talks.
He had his best years with the Los Angeles Lakers between 2004 and 2011. The team won NBA championships in 2010 and 2011 and Odom won the NBA's sixth man award during that second championship run.
Kardashian, 29, is best known for starring with her sisters Kim and Kourtney, and her mother, Kris Jenner, in the long-running reality TV series "Keeping Up With the Kardashians."
She also runs an upscale clothing store with her sisters and was featured in the short-lived reality series with Odom, called "Khloe & Lamar."
The two were married in 2009 in a large ceremony that was taped for the E! network, following a whirlwind engagement that was also filmed.
Kardashian laughed last spring when asked about critics who said that the marriage wouldn't last.
"I think everyone said it wouldn't last, but I can totally understand why," she said. "We knew each other for only 30 days and then we got married. ... I just felt it and same with Lamar. Thank God it worked because it very well could've gone the other way."
In recent episodes of "Keeping Up With the Kardashians," Odom hasn't been featured and the show has hinted at marital issues.
TMZ first reported Friday's divorce filing.
