They also played each other in the classic 2016 World Series in which Baez's Cubs prevailed in seven games. A year later, they shared the joy of playing for runner-up Puerto Rico in the World Baseball Classic.
Baez and Lindor have been back on the same field as the Cubs visited the Indians for a two-game series this week. On Wednesday, they got a moment to reminisce.
"We both got here at the same time, so we got to talk for a little bit," Baez said. "Everything is great between us. He congratulated me on the new baby. I actually asked him to sign a bat for me for the baby."
Baez, 27, is a two-time All-Star and was the National League MVP runner-up in 2018, but he calls Lindor the best shortstop in the game. Lindor, 26, is a four-time All-Star and two-time Gold Glove winner.
"I always looked to him as an example and learned a lot from him," Baez said. "We both moved to the United States at the same time. We come from the same place, so we have had pretty similar experiences. I make my own adjustments in my life, but whatever positive things from him, I am sure to pick it up.
"They compare us a lot back in Puerto Rico. They look at all the great shortstops. We are good, but he is a complete player just like me and (the Rockies') Trevor Story. I believe he is the best shortstop in the game right now. I believe he is the best, but I believe in myself too."
Wednesday was just the latest example of Baez praising Lindor. Just before spring training came to an abrupt halt in March, Baez told 670 The Score that Lindor is the only MLB player that he'd switch positions for. Baez became the Cubs' full-time shortstop in 2019 after previously splitting time between second base and shortstop.
"There are going to be free-agent shortstops the same year Frankie and I are," Baez said then. "I play other positions, and I would love to play with him. We had so much fun in the World Baseball Classic. We understood each other so well. It was an amazing experience. We will see how these things go. If someone wants to win and they offer us both contracts, I will play second base if he is the shortstop. He would be the only one I move positions for."
Baez -- who has previously said he wants to remain with the Cubs for his whole career -- and Lindor are both on a path to become free agents after the 2021 season. Of course, it could take an owner spending upward of $800 million on his middle infield to create one of the most exciting double-play combinations in MLB history.