According to Us Weekly, the couple has received the stamp of approval from their families.
"Kourtney and Travis have been spending a lot of time together, but they’re taking their time and trying not to move too fast," an insider told the outlet. "No one is surprised by their relationship."
The magazine's source added that the pair has "so much in common" with each other.
"They have big modern families [and they] both are dedicated to their kids," the insider explained. "They come from these modern families with modern relationships. Both of their families are supportive. It’s still very new, but they are both very excited by how easy it all has been."
The Poosh founder, 41, and Blink-182 drummer, 45, seemingly confirmed their relationship on Tuesday with a vague Instagram post from Kardashian, which features the two holding hands after Valentine’s Day weekend.
According to People magazine, Kardashian and Barker are longtime friends and have been seen with one another in Los Angeles in recent weeks.
They hinted at their relationship on Valentine's Day when they both shared photos of a lit fireplace on their Instagram Stories. According to the outlet, Barker also shared a photo of a diamond anklet, which could have been his gift for Kardashian.
Barker has been married twice -- first to Melissa Kennedy from 2001-02 before he was married to model Shanna Moakler from 2004-08. He and Moakler share two children: Landon, 17, and Alabama, 15.
Kardashian has never been married but was in a relationship with Scott Disick from 2006-2015. They share three children: Mason, 11, Penelope, 8, and Reign, 6.
Reps for Barker and Kardashian did not immediately respond to Fox News' request for comment.