Why Chris Pratt and Katherine Schwarzenegger's summer romance is heating up

Chris Pratt and Katherine Schwarzenegger’s surprise summer romance is still in full bloom — and sources say they are getting closer to each other by the day.

“It’s only been a couple of months, but they’re both serious about the relationship and hopeful for the future,” a source close to the couple tells PEOPLE. “Chris doesn’t just date to date, and neither does Katherine. She’s very excited.”

Since the pair, who were first introduced by Schwarzenegger’s mother, Maria Shriver (her dad is actor Arnold), were spotted enjoying a picnic together in Santa Barbara, Calif., on Father’s Day in June, the Jurassic World: Fallen Kingdom star, 39, and the author, 28, have been spending plenty of quality time together. They’ve been spotted riding bikes, going on multiple church dates together and hanging out with each other’s families—including Pratt’s son Jack, 6, with ex Anna Faris.

Though Pratt’s rep recently denied a report of an engagement, “Chris and Katherine are very happy together,” says the source close to them. “They’re very compatible and have a lot in common.”

For much more on Chris Pratt and Katherine Schwarzenegger, pick up the latest issue of PEOPLE on newsstands Friday.

Chris Pratt and Katherine Schwarzenegger are smitten after a date night at R+D Kitchen

“Family is very important to both of them, as well as their spirituality,” adds the insider. “She’s very, very sweet and maternal and great with his son.”

Meanwhile Faris, 41, has been happily dating cinematographer Michael Barrett, 48, for almost a year following her separation from Pratt in August 2017. The exes, who filed for divorce and requested joint custody of Jack last December, appear to be amicably co-parenting. They were recently photographed together with Jack multiple times before their son’s first day of school.

“They were all together for school activities,” says another source. “They are very friendly and seem happy when they are together with their son.”