Taylor Swift and Travis Kelce Are in 'Super Early Days' of Getting to Know Each Other: Source

"They're just hanging out, and there's no pressure," a source tells PEOPLE after Swift attended the Kansas City Chiefs' game on Sunday

Taylor Swift and Travis Kelce are taking it slow.

After the pop superstar attended the Kansas City Chiefs tight end's game against the Chicago Bears at Arrowhead Stadium in Kansas City, Missouri on Sunday, a source tells PEOPLE the pair are still in the "super, super early days" of getting to know one another.

"They're having fun," adds the insider, noting that Swift and Kelce had met prior to her attendance at the game. "This was Taylor's first time meeting his mom and dad, and everyone was enjoying themselves. She was super chill and low-key hanging out with his friends and family."

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Travis Kelce and Taylor Swift.

JC Olivera/Getty; Taylor Hill/Getty

The 33-year-old Grammy winner cheered on the Chiefs from Kelce's suite alongside the athlete's motherDonna Kelce. The pair could be seen sitting shoulder-to-shoulder and chatting and laughing together throughout the game.

Swift and Kelce, also 33, were captured on video as they walked together out of the building after his team's 41-10 win. Then, they drove off together in a car from the NFL star's personal collection, which was featured at 87 & Running's Kelce Car Jam, a charity event he participated in on Friday.

KANSAS CITY, MISSOURI - JANUARY 21: Travis Kelce #87 of the Kansas City Chiefs celebrates after defeating the Jacksonville Jaguars in the AFC Divisional Playoff game at Arrowhead Stadium on January 21, 2023 in Kansas City, Missouri. The Kansas City Chiefs defeated the Jacksonville Jaguars with a score of 27 to 20. (Photo by David Eulitt/Getty Images)
Travis Kelce. David Eulitt/Getty

Kelce "rented out a restaurant" for an intimate gathering with his friends and family, which Swift attended, after the game. "They were cute and normal, just hanging out and chatting," adds the source.

As for where things go next? "They're just hanging out, and there's no pressure," says the source.

A few days prior to Swift's appearance at the game, Kelce invited her to attend while appearing on The Pat McAfee Show podcast.

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Travis Kelce and Taylor Swift.

Douglas P. DeFelice/GettyMatt Winkelmeyer/Getty

On the podcast Thursday, host Pat McAfee asked Kelce if he wanted to "expand upon" the rumors that he and Swift are dating, which is "being talked about by the whole entire world right now." 

Though he wouldn't confirm at the time whether he and Swift had actually met in person, he did share that he "threw the ball in her court."

"I've seen you rock the stage at Arrowhead [Stadium],” he told McAfee of his conversation with the singer. “You might have to come see me rock the stage at Arrowhead and see which one's a little more lit."

"We'll see what happens in the near future," he added.

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