As it turns out, that team is the Tigers following last week's blockbuster deal, which sent Kinsler to Detroit in exchange for slugger Prince Fielder.
"I've been with the Rangers organization since I was drafted in 2003, so it's going to be a new journey for me," Kinsler said during a conference call on Monday. "But as far as the organization that I got traded to, I'm really excited. From the other side, it's always been a team that's really tough to play."
It's also a team that, like his former team, has had yearly World Series aspirations for much of the past decade.
As a member of the Rangers, Kinsler qualified for the postseason in three consecutive years (2010-12) and twice reached the World Series, falling in back-to-back Fall Classics in 2010 and 2011. The Tigers ended the Rangers' run as American League champions one year later, winning the 2012 pennant, only to be swept in the World Series at the hands of the Giants.
As Detroit continues its quest for its first title since 1984, Kinsler is confident that he can return to that big stage with his new club and, together, take home that coveted World Series trophy.
"You can tell they're in a 'win now' mode, and they have the pieces to do that," he said. "I'm glad to be a part of that, be one of those pieces. I'm prepared to do that, and I'm going to help this club the best I can."
Kinsler, who has $57 million left over the final four guaranteed seasons of his contract, was on vacation in Hawaii last week when he received news of the trade. The three-time All-Star was by no means hoping for a trade entering the offseason, but given the Rangers' abundance of options for the middle infield, he was anything but blindsided.
"There were definitely some expectations to be traded," he said. "In the baseball world today, it's very rare to have a player that stays with one team for his whole career. I was part of the Rangers organization for so long that I understand the way they work and the way they think. So I knew that this was definitely possible this offseason."
A prime candidate to assume leadoff duties for the Tigers, Kinsler brings with him a mix of speed and power. He has twice hit 30-plus homers in a season, connecting for 31 in 2009 and 32 in 2011. He stole at least 30 bases in each of those seasons and has swiped 20-plus bags in five of the last seven years.
In eight seasons with the Rangers, he hit .273 with 156 home runs, 539 RBIs, 748 runs and 172 stolen bases.
He hit in the leadoff spot in 662 of his 1,066 games with the Rangers, turning in a .346 on-base percentage and .813 OPS in those games. Though he is likely to continue hitting leadoff in Detroit, he is open to hitting wherever the Tigers need him.
"I've had experience [at leadoff], and I think they understand that," he said. "But I think in Spring Training we'll be able to hash that out and figure out what works best for the club. Wherever I'm hitting in the lineup, I'm going to be prepared and ready to contribute in that spot."
That said, he admitted that he has already thought about what it will be like to hit somewhere in front of two-time AL MVP Miguel Cabrera.
"Miguel has had everything in the world said about him as far as the greatness that he has as a baseball player, so I don't know what else I can add that hasn't already been said," Kinsler said. "If I have the opportunity to hit in front of him, I'm going to try to take advantage of that every day."
Kinsler touched base on a number of other topics, ranging from his excitement about playing up the middle with Jose Iglesias to the number he plans to wear, as the No. 5 he wore during his time in Texas is retired in Detroit in honor of Hank Greenberg.
But Kinsler said that picking a new number is the least of his concerns.
For now he's simply focused on getting to know his new teammates, as well as his -- and the Tigers' -- new manager, Brad Ausmus. Kinsler spoke to Ausmus following the trade and said he's looking forward to navigating the new Detroit experience alongside the first-time skipper.
"I know what he represents as far as the way he played the game during his time as a player, and catchers have very good reputations of becoming great managers," Kinsler said. "So I'm looking forward to it. It's kind of unique that his first year there is also mine, so we're both coming into a new environment. It's exciting."
The next step for Kinsler is to start forming similar bonds with his teammates. Other than brief in-game chatter over the past eight years, he doesn't really have any relationships with any current Tigers.
"I know the guys just from playing against them, so I'm not friends with them -- not yet, anyway," he said. "I'm excited to meet some new people and be part of a new team."