A source tells PEOPLE that the mother of three is in a place in her life "where she's ready for a relationship with a more mature guy."
"Kourtney and Travis have a long, long history and years of friendship," the insider says.
"They've felt like family for years, and she's really close with Alabama, who's just a cool rock star kid," the source adds of the Blink-182 rocker's 15-year-old daughter Alabama, whom he shares with ex Shanna Moakler. Barker, 45, and Moakler also share son Landon Asher, 17.
The source describes Barker as "a super smooth guy and women love him, but he's not a player. He's really, really nice, chill and is an adult."
"Kourtney is at a place in her life now where she's ready for a relationship with a more mature guy," the source says. "Her sisters love him."
Barker opened up about his relationship with Kardashian, 41, on Drew Barrymore's CBS talk show last week, saying that things come naturally between him and the reality star.
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"It just comes natural, it's like a maturity thing. And I also really like missing someone and cherishing the time that I spend with them instead of every day being with them, especially in the beginning of the relationship. I think missing someone is so important," he said of what it's like dating another parent.
Charles Sykes/Bravo/NBCU Photo Bank/NBCUniversal via Getty Images; ABC via Getty Images Kourtney Kardashian, Travis Barker
Kardashian — who shares kids Mason, 11, Penelope, 8, and Reign, 6, with ex Scott Disick — and Barker have known each other for years, but the Poosh founder didn't expect their friendship to become romantic, a source told PEOPLE last month.
"Kourtney is very happy with Travis. She wanted to confirm their relationship, because it's something positive," the source said after Kardashian made her relationship with Barker Instagram official. A source told PEOPLE in January that the duo had been "dating for about a month or two."
"She was single for a while and didn't expect that their relationship would turn romantic," the source said. "She feels very fortunate. She loves spending time with Travis."