Odom, 33, has had a cocaine problem for at least two years. The 29-year-old Kardashian reportedly does not want to be with him until he gets help and is clean.
Neither Lamar nor Kardashian have consulted a divorce lawyer, but an end to their four-year marriage may be in the works nonetheless. Kardashian has been uncharacteristically quiet about her marriage to Odom, even in talking to her family members.
Should they decide to divorce, a prenuptial agreement is in place to protect Kardashian, at her mother Kris Jenner's insistence.