Last week, the two called off their divorce, leading many to assume that they were back together.
Khloé tells People, "It's out in the media that we are back together, but I wish people understood that's not in our thought process right now. There are too many other important things, too many medical things. It's not even in our brains, thinking about us as a couple or having a relationship right now."
She reiterates, "It's not anything sexual or intimate. I want to be his support system. Tragedy does make you reassess a lot of things, but when it comes to our relationship, it's the same, except I'm here supporting him fully."
Kardashian also admits she loved Odom, even when they were no longer a couple. "I loved him always, and I will always love him. I don't believe love is fickle. I believe when you love someone, you are allowed to love from afar. You don't have to be with that person in order to love him."
When Lamar was fighting for his life, Kardashian put the brakes on her relationship with James Harden to be by Lamar's side. Now, she is thinking only about Lamar's recovery. She says, "I'm not trying to get married tomorrow to anybody. It's just bad timing to proceed with that right now. And also, for medical reasons, it's just smarter that gets [put] on hold for a minute. But that does not mean I'm back with Lamar. That's a whole other thing that only time will tell. I can't tell you what tomorrow brings."
On the topic of Lamar’s health, she reveals, "The fact that he woke up was definitely a sigh of relief for everybody. Every hour is different. It goes up and it goes down, but he's awake. He's alive, and that's all I wanted, was for him to be okay."
She adds, "There is a very long road ahead of [Lamar]. He has to walk that road by himself, and, most importantly, he has to want to walk that road. I will be there supporting him every step of the way."
To read more of Khloé’s interview, pick up the latest issue of People!