"Katherine and Chris have been on a few dates," the source says. "The two really enjoy their time together, but it's still in the early stages. Chris was introduced to Katherine by one of her family members and the two hit it off."
"Chris is focused on the press of his movie and his son Jack, but when he does get some free time, he spends it with Katherine," the source adds.
Pratt shares Jack with actress Anna Faris, whom he split from last August. The source says that the 39-year-old Jurassic World star is taking his time when it comes to his budding relationship with Schwarzenegger.
"Chris and Anna split about a year ago, and Chris wants to move slow," the source says. "He's in no rush for a relationship."
Meanwhile, despite her famous parents, Schwarzenegger has largely stayed out of the spotlight growing up. For six things to know about the the private brunette, watch the video below: