Kim, who is in a relationship with Kanye West, is said to be 'very supportive' of her sibling and her relationship with Odom, reported E! online.
Recent reports have claimed the couple's divorce is imminent after rumours of the basketball player cheating with two different women while on the road and his alleged crack cocaine use - but Khloe's sister hopes they can move past their problems.
"She only wants what's best for Khloe ...Kim would like to see them work it out. She knows how much they love each other.
Everyone in the family feels divorce should be the last option," a source said. Khloe apparently kept the details of her marital problems a secret from her family, and the insider said Kim was 'shocked' to learn of the extent of the issues.
"Khloe did keep her marriage issues with Lamar a secret from her family for quite some time - no one knew," it added.