Travis Kelce is already thinking about a possible name for his future baby amid his romance with Taylor Swift. During the latest episode of his “New Heights” podcast with brother Jason Kelce, the Kansas City Chiefs tight end teased what he “might” name his first child.

“I might name my first kid Conan. I might,” Travis, 34, told special guest Arnold Schwarzenegger while discussing the actor’s films during the Wednesday, April 3, episode. The name is a reference to 1982’s Conan the Barbarian, in which Arnold, 76, plays a barbarian warrior who seeks revenge for the death of his parents on the leader of a snake cult.

This wasn’t the NFL star’s first time hinting at his future children on the podcast. Last month, Travis created a buzz about his and Taylor’s potential future family during a discussion about 7-foot-4 San Antonio Spurs star Victor Wembanyama.

“You can’t tell me that dude wasn’t made in a f–king lab over there in France,” he told Jason, 36, on the March 19 episode. “Lab-grown diamonds, that’s a lab-grown f–king NBA player. Can’t wait til I f–kin’ make one.”

Jason immediately caught on to his brother’s sly remark and knew the frenzy it would cause among fans of the couple. “Don’t do this. Do not give any of these other conspiracy theorists anything else to latch onto, please,” he joked.

Travis and Taylor, 34, quietly started their relationship in July 2023 after he attended one of her Eras tour shows and shouted her out on the podcast. They went public with their romance in September 2023, showing support for each other at football games and concerts as much as possible. Now, both the Chiefs tight end and pop star are both on a break from work — the NFL is in its offseason and Taylor’s Eras tour is on a brief hiatus — and a source exclusively told Life & Style in March that they’ve been “testing the waters of living under one roof.”

“It seems to be going very smoothly. He moved into her Los Angeles mansion while she’s on break from her tour, they’re nesting and loving it,” the insider said.

And not only is living together going well, but it’s possible an engagement and family plans aren’t too far down the line. Another source exclusively told Life & Style that, during the couple’s recent vacation in the Bahamas, “Travis told Taylor he wanted to spend the rest of his life with her, and she told him she feels the same. It wasn’t an official proposal, but they’re committed to each other, and they spent the weekend celebrating in paradise.”