"Scott is not totally out of the picture," a source close to Kardashian tells PEOPLE. "She hasn't made a final decision. Right now, she's just living day to day. She's not begging him to see the kids, but she also hasn't definitively said 'I'm never letting him back again.' "
Kardashian, 36, and Disick, 32, were recently spotted out together for the first time since their breakup. The reality stars, along with two of their three children – Mason, 5, and Penelope, 3 – enjoyed lunch together Thursday at the Beverly Hills Hotel.
"For the first time, she's taking a hard look at what her new reality could look like," the source says of Kardashian. "Before, she just assumed nothing would really change, but now there's a strong possibility of life without him, and that's a scary thought for her. She was doing most of the work already, but at the end of the day, she would still turn into a single mom of three kids."
Besides Mason and Penelope, Kourtney and Disick share baby boy Reign, 7 months.
Though the mom of three is said to have been heartbroken over the split, Kardashian seems to be doing as well as expected.
"She's figuring it out and taking it as it comes," the source says.