According to the source, Pratt, 39, "has been letting Katherine take charge" of the arrangements for their big day.
"They both seem very happy," the insider says of Pratt and Schwarzenegger, 29. "They live together and are just so cute."
Pratt and Schwarzenegger announced their engagement on social media back in January after seven months of dating. It'll be her first marriage and his second after he and Faris announced their split in 2017.
Last week, Schwarzenegger opened up about her soon-to-be "I dos" to Entertainment Tonight, telling the outlet that the nuptials will be a family affair.
"I feel like we're all really involved in wedding planning," Schwarzenegger said at the premiere of the new IMAX film Superpower Dogs. "I think that, you know, for me my family is very involved. I'm very involved, [Chris is] very involved…So it's a great combination of everything and just a really exciting and fun [time]."
She added to ET, "I'm very happy in all areas of my life and I feel really blessed and really lucky."
The Christian faith was one of the things that bonded Pratt and Schwarzenegger, so it is no surprise that religion will be front and center at their wedding. "They're going to want a religious wedding," an insider told People in January. "I know that Chris does, and I assume that she does, too. God is going to be a part of this marriage."
Sharing a hint about their possible wedding date, he mentioned they were "maybe" thinking of a "fall, winter kind of thing," before adding that he and Schwarzenegger still have "a lot to get done."
No matter what the couple decides on, they've already got the approval of Jack. Asked how his son is taking the big news, Pratt said he was "so thrilled."