The reports come as Khloe lashed out on Twitter on Sunday, tweeting:
'Really hard to sit here and listen to people talk s*** about my family! F*** you and shame on you! I'm too protective for this s***!'
The 29-year-old reality star has been subject to several rumours that her marriage to NBA star is in trouble, following allegations that the 33-year-old cheated on Khloe with two different women.
But sources have revealed that the real reason behind the married couple’s relationship trouble is because Khloe is said to believe that her husband has a drug problem.
Despite winning two championships with the Los Angeles Lakers, sources have revealed that Odom resumed using drugs after the basketball season had ended.
The Kardashian family allegedly staged an invention to convince Lamar to return to rehab earlier this week, following his unsuccessful visit in August 2012.
According to the American website, Lamar refused, prompting Khloe to throw Lamar out of the family home. He was spotted on Wednesday overlooking a man loading large amounts of luggage into his car.
A source revealed, ‘Khloe is more concerned about saving Lamar than ending her marriage’.
A spokesperson for the basketball star told the website on Sunday that Lamar was fine, but that he would not reveal his whereabouts.
Khloe and Lamar got married in 2009 about a month after meeting each other.