The couple has been carrying on a private romance as of late.
"They're still taking things slow," the source says of the pair. "She's enjoying this time and seeing where things go. She is being mindful of her kids as her main priority is always being a great mom."
In the last month, Kylie, who's mom to Stormi, 5, and Aire, 1, has been spotted at the 27-year-old actor's Beverly Hills home. The 25-year-old cosmetic mogul even attended a family barbeque, with her sister, Kendall Jenner, and Timothée's sister, Pauline Chalamet, both on hand.
Back in April, a source told ET that Kylie and Timothée had begun dating. "They are keeping things casual at this point. It's not serious, but Kylie is enjoying hanging out with Timothée and seeing where it goes," the source said. "It's been really fun for her because it feels a lot different than her past relationships. It's new and exciting for Kylie and she's having a lot of fun."
The source additionally noted that "Timothée is also friends with Kendall, so it's been easy for Kylie to integrate him into her life."
The next month, another source told ET that Travis Scott, Kylie's ex and the father of her two children, "is not thrilled about Kylie moving on." However, the source said the exes "are still cordial and focused on co-parenting and being the best parents they can be."
As for what the rest of her loved ones think of the romance, the source said, "Her family thinks it's great that Kylie is doing her thing and they are supportive."
"Kylie and Timothée are casually seeing each other, but are trying to keep it low-key. They are becoming more comfortable with each other, but Kylie wants to take things day by day and see where it goes," the source added. "Timothée loves that Kylie is such a hands-on mom and a boss. He appreciates her confidence and thinks she's incredibly beautiful."