The 33-year-old reality star got close to Thompson on Sunday while enjoying a summer day by the pool with the 26-year-old NBA player.
"All my love," she captioned the picture for her 68.6 million Instagram followers.
Kardashian and Thompson were first linked in October following their respective splits from James Harden and Jordan Craig, who shares 7-month-old son Prince with Thompson. Kardashian said in a mid-June episode of Keeping Up with the Kardashians that Thompson wants "five or six" kids with her.
"He wants to have kids now," the star told sister Kim Kardashian.
"Tristan and I definitely talk about starting a family. He wants to have five or six kids with me and that's lovely. We could start at one and we could grow from there," she added in a confessional shot. "It's scary. It's a really big step."
"She really wants a baby," a source said of Kardashian, who is aunt to six nieces and nephews, including Saint West and Dream Kardashian. "She hopes it will happen soon."
"[She] is very happy and positive about her future with [Tristan]," the insider added. "She is absolutely hoping for an engagement."
Kardashian finalized her divorce from Lamar Odom in December after initially splitting from the former NBA player in 2013. Odom confessed he was a "scumbag" to the reality star while discussing his drug use in a recent essay for The Player's Tribune.