Kardashian, 41, "loves having Travis sleep over, and sometimes he'll stay the whole weekend," dishes an insider, who says the Blink-182 drummer, 45, gets along famously with her children Mason, 11, Penelope, 8, and Reign, 6.
"Travis has been a friend of the family for years, so the kids have pretty much known him their whole lives," explains the insider. "They'll do fun stuff together, like hiking or playing video games, and Travis loves making breakfast and showing off his pancake-flipping skills."
The musician, who shares children Landon, 17, and Alabama, 15, with his ex, Shanna Moakler, "is spending so much time at Kourt's place that he's moved a bunch of his stuff in to make it easier for them to visit him there," the insider adds. "It's an easy transition since he also lives in the neighborhood. Everyone's convinced they'll be living together full-time before you know it!"
(We're sensing a KUWTK spin-off in the making!)
However, while the romance between the two continues to grow, things between Kardashian and Barker's ex are clearing causing a stir.
As OK! previously reported, a social media feud between the two ladies began when Moakler appeared to "like" a comment on her Instagram that read: "Shhhhiiiii that broad don't got nothin' on you. Travis downgraded big time." The comment was in reference to the KUWTK star and was posted a few days after her and Barker's relationship went Instagram official.
Moakler later said that she didn't mean any harm, but it was too late — as Kardashian decided to quickly clap back.
"It's no wonder we've made a daily — or several times daily, or every hour — habit of checking in [on] our exes, and our exes' exes, their new lovers, friends, acquaintances, and so forth," Kardashian wrote in a Poosh post. "It's not healthy, it's not helping us move on, and unfortunately, it's all too easy."
Naturally, Moakler wouldn't let things rest. She appeared to slam the new relationship between her ex and Kardashian by posting a quote to her Instagram Story that read: "Stop complaining about your life. There are people out there dating your ex," adding a crying-laughing and a wink emoji.