Kylie and Travis were together on and off before calling it quits in January.
A source tells ET, "Travis is not thrilled about Kylie moving on, but they are still cordial and focused on co-parenting and being the best parents they can be."
Kylie, 25, and Travis, 32, have been in an on-again, off-again relationship since 2017. In January, the pair -- who share children Stormi, 5, and Aire, 1, decided to take a break from their relationship after leading different lifestyles.
In April, ET confirmed that the Kylie Cosmetics founder had recently begun dating Timothée. The source tells ET that the Oscar-nominated actor and the reality TV star are keeping things casual.
"Kylie and Timothée are casually seeing each other, but are trying to keep it low-key," the source says. "They are becoming more comfortable with each other, but Kylie wants to take things day by day and see where it goes. Her family thinks it's great that Kylie is doing her thing and they are supportive."
The source adds, "Timothée loves that Kylie is such a hands-on mom and a boss. He appreciates her confidence and thinks she's incredibly beautiful."
Kylie and Timothée have yet to confirm anything themselves or share hints of their blossoming romance on social media. The pair reportedly met through Kylie's older sister, Kendall Jenner.
Last month, Kylie and Timothée attended the Coachella Valley Music Festival, and still managed to stay under the radar. A source told ET at the time, the duo isn't ready to make things public.
"Kylie decided she didn’t want to make things public with Timothée this past weekend at Coachella," the source explained, "and really just wanted to chill and have fun with her friends."