A source tells PEOPLE that Kardashian, 33, is house hunting with the 26-year-old Cleveland Cavaliers player. According to the source, they’re not moving in together officially just yet, but Thompson (who has a home in Cleveland) is looking to rent a place in Los Angeles.
“They live at Khloé’s Calabasas house right now,” says the source, explaining that Thompson is hoping to land a home closer to the downtown area.
“He thinks the drive from Calabasas to L.A. is too far every day,” says the source. “When they go out in L.A., they want a second house that’s closer.”
A real estate source tells PEOPLE that Kardashian and Thompson toured several properties earlier in the week but haven’t decided on one yet.
As for Kardashian? She’s “just the happiest,” says the source close to the star. “She loves spending every day with Tristan.”
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The news doesn’t exactly come as a surprise, considering the fact that the romance between Kardashian and Thompson, which started in September, has only been heating up in recent months — and Kardashian has made it clear she’s ready for the next step, revealing on KUWTK in June that she’s stopped taking birth control.
“Tristan and I definitely talk about starting a family,” she said. “He wants to have about five or six kids with me and that’s lovely. We could start at one and we could grow from there.”
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But should we expect wedding bells first? A source recently told PEOPLE that Kardashian is “very happy and positive” about their future together.
Added the insider, “She is absolutely hoping for an engagement.”