Multiple sources familiar with the situation told TMZ Odom has had a drug problem for the past two years and even went to rehab last August under pressure from Kardashian.
Odom left rehab after about three weeks, and even though he got clean for the following season with the Los Angeles Clippers, the player allegedly returned to hardcore recreational drugs after the season was over, the celebrity gossip website said.
Odom was spotted by photographers Wednesday leaving his home with several bags and suitcases.
Neither Odom nor Kardashian has filed for divorce.
"Khloe is more concerned about saving Lamar than ending her marriage," a source told TMZ.
Meanwhile, Kardashian was spotted Friday by photographers going to the gym without her wedding band or engagement ring, Entertainmentwise.com reported.
"Khloe definitely had the ring with her but while working out, she took it off," a source alleged to HollywoodLife. "But she knew she would be getting photographed on her way out and she wanted it to happen so she could give Lamar a wake-up call."