Taylor Swift and Travis Kelce Are Giving Their Romance a 'Real Try' with 'Insane' Schedules (Exclusive Sources)

It seems Taylor Swift and Travis Kelce are really enchanted by one another.

A source reveals exclusively to PEOPLE that the pair are giving romance "a real try," despite both of their schedules being "actually insane."

"She's the biggest star in the world and it's no secret dating an athlete is very tough, but they've been texting and talking on the phone between the pockets of time they get to spend with each other," they say.

The source adds that the Kansas City Chiefs tight end, 34, is "still very focused" on the team and is "a pro at compartmentalizing."

"There's not some looming date like, 'Oh, she's going back on tour' and 'his football schedule is getting crazy.' They'll figure it out. He's said it himself, he knows what he signed up for with this attention, but they've spent time under the radar too. They're giving things a real try," the source says.

Swift, 33, and Kelce made all of New York City shimmer this weekend as they were spotted spending time together.

During their first public, hand-holding date night — which also coincided with their surprise Saturday Night Live appearances — the NFL player and "Anti-Hero" singer attended the show's afterparty at Catch Steak following the season 49 premiere of SNL on Saturday night.

“Taylor and Travis were there all night and they were so smiley, they were so happy,” an insider previously told PEOPLE. “They were so talkative. They were really fun. They talked to every single person in the room that talked to them.”

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And on Sunday evening, the couple were spotted walking hand in hand as they left the Waverly Inn restaurant after dinner at the West Village staple.

"Taylor's unlike anyone Travis has dated before," the source explains. "It was very unexpected for his friends, but he's so into her and very, very happy."