Kardashian even hired a private investigator to make sure her husband went to rehab, the report alleged.
"Our sources say Lamar constantly threatened to leave and Khloe made several visits to prevail upon him to stay. We're told after 3 weeks, Lamar left for good," the gossip site said.
The drug abuse allegations come after weeks of rumors that Odom cheated on his wife with an attorney named Polina Polonsky.
Though the 29-year-old television personality has kept quiet about split reports -- favoring more cryptic tweets about strength and privacy -- she finally fired back in an expletive-laden tweet on Sunday.
"Really hard to sit here and listen to people talk sh** about my family!" Kardashian tweeted. F*** you and shame on you! I'm too protective for this sh**!
Family matriarch Kris Jenner has denied rumors of a divorce.
"Khloe and Lamar are absolutely not getting divorced. There's been no talk of divorce," she told TMZ earlier this month.