Taylor Swift and Travis Kelce ‘Are Not in the Wedding Planning Phase Yet’ After Engagement: Source

Taylor Swift and Travis Kelce are still glowing from their recent engagement.

“Taylor and Travis have been in celebration mode ever since the engagement,” a source close to the couple told PEOPLE. “They are not in the wedding planning phase yet.”

The Grammy-winning singer and the NFL star, both 35, shared the big news on Aug. 26 in a joint Instagram post, almost two years after making their relationship public.

“Right now they just want to enjoy being engaged and they are going to take their time with it,” the source explained. “It has been a relief not having to keep it a secret anymore, and they are glad it is out in the open.”

In their announcement, the couple wrote, “Your English teacher and your gym teacher are getting married 🧨,” ending with a dynamite emoji, a nod to their playful “TNT” nickname.

They also posted a carousel of photos showing the moment Kelce proposed in his backyard. The Kansas City Chiefs tight end set the scene with a beautiful floral arrangement about two weeks before the couple revealed the news publicly.

Kelce’s dad, Ed, shared on Australian radio’s The Jimmy & Nath Show with Emma how the proposal unfolded. “They were going out to dinner and she was ready to go and he said, ‘Let’s go out in the garden on the patio and have a glass of wine before we go,’” Ed recalled. “I think she knew something was up because as they walked out there, she could see, suddenly, there were a lot more flowers out there.”

“These are two young people madly in love with each other, and I think this is great,” Ed added.

The couple’s families are just as happy. A source previously told PEOPLE, “Both families are overjoyed. There were toasts, happy tears and everyone is thrilled for them.”

Kelce’s mom, Donna, has already started saving memories from the engagement. “Donna is already saving little things from this time like photos, notes and flowers,” the source said. “She is very sentimental about it. She wants to remember every detail, so she has been holding onto mementos from their first days as an engaged couple.”

The engagement also comes shortly after Swift appeared on the New Heights podcast — which Kelce co-hosts with his brother Jason — to announce that her new album, The Life of a Showgirl, will be released on Oct. 3.