Although the couple isn't looking to move in together officially just yet, the 26-year-old Cleveland Cavaliers player reportedly wants to rent a place in Los Angeles.
"They live at Khloe's Calabasas house right now," the source said, explaining that Thompson is hoping to find a place closer to the downtown area.
"He thinks the drive from Calabasas to L.A. is too far every day. When they go out in L.A., they want a second house that's closer."
A real estate insider told People that Kardashian and her boyfriend toured multiple properties together earlier this week; however, they haven't reached a decision.
Kardashian is "just the happiest" about her growing relationship with Thompson, said the source close to the reality TV star and Revenge Body host.
Late last month, the NBA player threw her a surprise birthday party for Kardashian that she called "incredible" and "dream like." Thompson also shared a montage of photo-booth snapshots from the party on Instagram, gushing about how much he loves and cherishes Kardashian.
"She loves spending every day with Tristan," the source told People of the two lovebirds, who have been dating since Fall 2016.
Kardashian and Thompson have seemingly been inseparable ever since becoming romantically involved last year.
"She is absolutely hoping for an engagement," another source previously told the magazine. "[They] talked about both a wedding and a baby... [Khloe] really wants a baby and she hopes it will happen soon."
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"He wants to have kids now... Tristan and I definitely talk about starting a family," Kardashian said in a confessional on the show. "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. It's scary. It's a really big step."
Thompson is already dad to seven-month-old son Prince, whom he welcomed with his ex-girlfriend Jordan Craig in December.