The reality star, 31, sat down for an interview with Complex magazine for the August/September issue and opened up about her relationship with Odom, 35.
"I talk to Lamar as often as I can, which is inconsistent, but not on my terms," Kardashian told the magazine. "When you genuinely feel like that was the right relationship, you're supposed to give it all you can. That's what marriage is about. It's not, 'Let's see if it works, if not we always have divorce.' I am not one of those girls. You took a vow before God and you're supposed to abide by that."
The Keeping Up with the Kardashians star and Odom wed in 2009 just one month after meeting. After he relapsed with his substance abuse problems and cheated on Kardashian, she filed for divorce in December 2013.
The interview took place before the papers were signed this month, and Kardashian maintained at the time that she wasn't "rushing" the divorce because she wasn't "looking to get married tomorrow."
"Lamar is genuinely one of the best people I've ever met, and everyone says that when they meet him. I think Lamar's going to always be that person [for me] but that's what made it so special," she continued. "Even if I had it for five years or whatever, it was the best ever and I'm grateful I did. Some people don't get that ever and I had that magic for a long time."
The reality star revealed that she misses Odom "every day."
"I miss what we had – things we got to do together are just memories. I like looking back and holding on to that stuff," she said. "I definitely miss it, and there's times I'll get so sentimental and so sad, but this had to happen for some reason. I'll figure it out over time, someone will give me that answer eventually."
Kardashian also opened up about her relationship with ex-boyfriend French Montana, who she was on-again, off-again with for several months after splitting from Odom.
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"I'm friends with him," she said. "He's a great guy, super funny, a sweetheart."
While she doesn't exactly consider him a "rebound" and wouldn't want to "discredit French at all," Kardashian did admit that she wasn't ready to be in a relationship at the time.
"I needed time on my own to digest everything that's happened. I went from Lamar to just distracting myself," she said. "I was very honest with French about that – I feel bad. I don't think it's fair for me to lead somebody on, or for me to act like I'm in this perfect headspace if I'm not. With love you don't mislead or play around, so if you're not perfectly clear, just be honest about it."
Kardashian was most recently linked to Houston Rockets shooting guard James Harden.