At the time, Jeter was 20 years old and had played in just 15 big league games, all of those for Buck Showalter during the 1995 season.
The Yankees had some veteran shortstops on the roster during the spring of 1996, so Torre knew his bosses, especially Gene Michael, had to be mighty impressed with Jeter to simply hand him the job.
Because it was the Yankees and the pressure to win big is constant, Torre watched Jeter with particular interest during that spring of 1996.
Jeter didn't have a particularly good spring, but Torre saw something emerge, something about Jeter that has endured in his heart and mind.
"He never changed even when things weren't going his way," Torre said. "He never rushed. He never panicked. He just felt comfortable and took care of his business."
To Torre, that attitude revealed an inner-toughness and confidence, a feeling Jeter had that he was plenty good enough to play in the big leagues.
Jeter homered on Opening Day in 1996, and he was on his way to constructing one of the great careers ever.
Along the way, he and Torre developed a mutual respect and a friendship that endures to this day.
They had breakfast shortly before this Spring Training, and Torre's message was simply: "Enjoy this season. Accept the fact that people want to thank you for what you've done."
All these years later, one of the more remarkable aspects of Jeter's career is that he has played for just three big league managers.
He broke in with Showalter in 1995 and played 15 games. Showalter has the distinction of being the last guy to tell Jeter he was being sent back to the Minor Leagues. Later that season, he was the guy who wrote Jeter's name onto a lineup card for the first time.
"He's somebody baseball should be proud of," Showalter said. "He understands the responsibility that comes with his tenure here. I was lucky. It was an honor. You think about all the time he spent there, he never did anything that embarrassed his family, his team, his teammates, the organization, the city. That's real hard to do."
Beginning in 1996, Jeter and Torre were side by side for the next 12 years. They won four championships, 1,173 games and had a .605 winning percentage.
Their first playoff appearance was in 1996, and Torre remembers the error Jeter made in one of the games.
Reporters asked Torre if he was going to speak with this kid, to check his mental state and make sure his confidence was unshaken.
"I was thinking about that," Torre said, "and as Derek left the clubhouse, he stuck his head in my office and said, 'Mr. Torre, get your rest because tomorrow will be the biggest game of your life.'"
Torre smiles at the retelling of the story.
"I knew he was okay," he said.
But there were other moments.
Once occurred when Jeter got thrown out in an ill-advised steal of third. When he returned to the dugout, he went directly to Torre and wedged himself between the manager and his bench coach, Don Zimmer.
"I kick myself because I should have given him the red light," Torre said. "But when he came and sat between me and Zim, that was his way of saying, 'Okay, let me have it.' He was going to hear what we had to say and then move on."
The Yankees won the first of their five championships with Torre and Jeter together in 1996. Early the next season, Torre wanted to check on his young guy.
"You know, it's New York and he's just won the World Series and he's a good-looking single guy," Torre said.
He wanted to see if quick success had gone to his star player's head.
"I think our conversation was about a minute," Torre said. "I had no doubt."
Jeter got his third manager at the start of the 2008 season when Joe Girardi took over. They've been together as player and manager for 1,130 games and have a .571 winning percentage. They won the 2009 World Series.
Girardi first met Jeter in 1996 when both were players. His first recollection was of a relaxed kid.
"I remember him walking through the dugout singing," Jeter said. "He was a young kid who was talented but extremely relaxed. He had a smile on his face. He was energetic. Nothing seemed to faze him. I was just like, 'It's not that easy to relax.' It really isn't. He had the ability to do it, and that's been a huge part of his career. That's why he has been able to come up with so many big plays."
Girardi has been asked to sum up Jeter's career countless times this season. In the end, it seems pretty basic. He had great talent and an even better attitude.
"There was always a smile and a happiness to play the game," Girardi said. "That's what you want in your players. He was always prepared. He always tried to do the right thing, whether it was in how he played or something he felt needed to be said to a teammate. I consider it an honor to have managed him."