She previously admitted: "I love Lamar to death. He is the love of my life. We had a fantastic marriage. Do I wish he had tried harder? Yes. Do I think that he maybe didn't have the energy to fight because he was fighting so many other things? Yeah."
Kardashian has been by Odom's side since he was found in extremely critical condition October 13 at the Love Ranch brothel in the rural community of Crystal, Nevada, and hospitalised in Las Vegas.
Her ex-boyfriend, rapper French Montana, has praised the reality star for supporting Odom.
The pair dated after she split from her husband, and despite parting ways earlier this year, Montana only had kind words to say about his former flame.
"It's a beautiful thing, what she's doing," he told New York Daily News' Confidential column.
"I feel like every woman should do that."
At the time of Odom's medical emergency Kardashian was dating another basketball player, James Harden.
Sources claim he stepped aside to allow his girlfriend to be with her husband.
Odom regained consciousness Friday and was transported to a facility nearer his home in Los Angeles on Monday.
Kardashian posted a statement to her website Monday saying he had made "incredible strides" at Sunrise Hospital and Medical Center in Las Vegas and thanking the doctors and nurses "for their kindness and diligent work".
The hospital and Odom's relatives have not revealed his prognosis, but the family has hinted at a long road ahead, saying they realize his "continued improvement" won't be easy.
The brothel said workers saw him drink alcohol and take supplements sold as "herbal Viagra".
The Food and Drug Administration issued a warning in 2013 against one brand he took, Reload, after it was found to contain sildenafil, the active ingredient in prescription Viagra.
He also told at least one of the women that he had done cocaine, but the brothel says it did not see him take any drugs.
Love Ranch owner Dennis Hof has said that Odom arrived October 10 for a four-day stay and spent US$75,000 on two women who accompanied him in a VIP suite.
Test results from blood samples obtained through a warrant still are pending, and authorities have not ruled out the possibility of taking action against the brothel or Odom.
- AP
