The reality star and the rock star may be thinking about their long-term future.
A source tells ET, "Kourtney and Travis really recognize now more than ever how special their relationship is and how fortunate they are to spend their time together whether it's just the two of them, with friends or with their families."
"They could also definitely see themselves ending up together one day and it's really whatever makes Kourtney happy," the source says, adding that for the time being, they are "just living in the moment and enjoying each day."
However, the source says they are "closer than ever," which means that for the 42-year-old reality star and the 45-year-old drummer, "Building a future together in a more permanent respect could likely happen."
"They feel like their biggest accomplishment thus far is how seamlessly they've integrated their families together," the source adds. "That's always been very much a focus for both of them and they feel proud that everyone can be supportive of their happiness."
Kardashian is the mother of three kids -- 11-year-old Mason, 8-year-old Penelope and 6-year-old Reign -- whom she shares with ex Scott Disick. Meanwhile, Barker shares two children with ex-wife Shanna Moakler -- 17-year-old Landon and 15-year-old Alabama.
"Their kids have all gotten a lot closer and both sets of kids think Travis and Kourtney are awesome," the source adds. "Kourtney gets along great with Travis' kids and the same goes for Travis with Kourtney's kids. They have all known each other for a very long time and the rest of Kourtney's family loves Travis too. They adore how he treats Kourtney and how he always puts her and their families first."
Another source previously told ET last month that the pair has been talking about engagement and marriage.
"Travis would absolutely love to tie the knot with Kourtney, but Kourtney hasn't been sure that's the step she wants to take in their relationship right now," the source said at the time. "She is extraordinarily happy and doesn't feel the need or want the pressure of getting married."
For more on their blossoming romance, check out the video below.