Taylor Swift and Travis Kelce may have shared their engagement news with the world, but their actual wedding won’t be a such a public affair.

A source tells PEOPLE in this week’s issue that the pop star and the Kansas City Chiefs tight end “want to keep it more private” when they tie the knot.

“It will definitely be a private affair and not a spectacle,” the source says. “They both have a close circle of friends, and they’ll respect their privacy.”

Swift and Kelce, both 35, announced their engagement on Instagram on Aug. 26 after two years of dating, sharing sweet photos from the proposal with the caption, “Your English teacher and your gym teacher are getting married.”

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Kelce popped the question with an old mine brilliant cut diamond — a ring the source says Swift is “still showing off.”

“She’s incredibly happy,” the source adds. “It’s all just perfect.”

The engagement is the cherry on top of an exhilarating era for both Swift and Kelce, who recently kicked off his 13th NFL season with the Chiefs. Though the team dropped their season opener to the Los Angeles Chargers in São Paulo, Brazil on Sept. 5, they’re set for a Super Bowl rematch versus the Philadelphia Eagles in Kansas City on Sept. 14.

Swift, meanwhile, is gearing up for the highly anticipated Oct. 3 release of her forthcoming 12th album The Life of a Showgirl, which she worked on in between Eras Tour stops, she said on Kelce’s New Heights podcast.

“This album is about what was going on behind my scenes in my inner life during this tour, which was so exuberant and electric and vibrant,” she said. “I’m so proud of it, and it just comes from the most infectiously joyful, wild, dramatic place I was in in my life. That effervescence has come through on this record.”

As for wedding planning, the couple are taking things one step at a time. Kelce said on New Heights that he hasn’t thought for “one second” about a bachelor party, but promised that it’s “gonna go crazy” when they do get to wedding planning.

“That,” he said, “is the next step.”