The 32-year-old reality star confirmed her romance with the 25-year-old NBA player on Thursday's episode of Jimmy Kimmel Live, revealing she's "very often" in Cleveland to visit the Cavaliers power forward.
"I live here [in Los Angeles] but I'm there very often. Very often," Kardashian told host Jimmy Kimmel. "I actually really like it [there]. I like just, like, having my routine and being a little more under the radar."
"The first week I was there, me and my friends went to the gym and then we went to Target, and we were in the car and we were like, 'Don't you like that there's no paparazzi here?' I said, 'I love it. No one even notices me,'" she recalled.
"I get out of the car and someone was like, 'Oh my God, you should get paid to be a Khloe Kardashian lookalike. You look just like her.' I was like, 'You're so right, I should!' Why would someone think I'm at Target in Cleveland? No one would think that," the star said. "[I was] under the radar."
Kardashian and Thompson were first linked in September after a getaway to Mexico. The pair were spotted kissing Sunday at the Cleveland Cavaliers Halloween party, where they dressed as Marvel characters Storm and Black Panther.
"Khloe has been spending a lot of time in Cleveland with Tristan," a source told People last week. "She's very supportive of him, and they are getting serious. They really dig each other a lot, and she's planning to spend more and more time out there with him."
Kardashian reached a settlement in her divorce from husband Lamar Odom in October. The star had filed to end her marriage to the former NBA star again in May after putting proceedings on hold due to Odom's hospitalization.