Rivera was considered an emerging talent in the team's bullpen then, but he hadn't yet been anointed as John Wetteland's setup man in what would play out to be a World Series season. Instead, Rivera packed his bags to head north as the club's long reliever.
"I remember excitement. It was a great time," Rivera said. "It has been a long time. It doesn't seem like that, but it has been a long time, yes."
As he enters his age 42 season -- possibly his last -- the man who would become the game's all-time saves leader was an overshadowed piece back then, falling into the backdrop of a typically tumultuous Yankees spring.
George M. Steinbrenner was still at the helm, having hired a new manager with a losing career record that no one seemed quite sure about. Joe Torre hadn't yet earned his pinstripes, figuratively speaking, and Tino Martinez was ending an era by taking over first base from the beloved Don Mattingly.
The Yankees were also carrying a rookie shortstop, Derek Jeter, and Steinbrenner wasn't completely sold on him. That spring, the Yankees quietly discussed a trade that would have imported Mariners shortstop Felix Fermin for Rivera or pitcher Bob Wickman, proof that the best deals are sometimes the ones never made.
Those details are spotty to Rivera all this time later; compiling 603 saves, plus 42 in the postseason, and climbing to the top of the baseball world on five occasions tends to have that effect. He recalls going about his business dutifully and wasn't surprised when Torre included his name among the players heading north.
"Not really," Rivera said. "I knew I had made the team. I kind of expected it, so that was it. Nothing different."
Those who have been around Rivera from the beginning are amazed that the years of success, living at the game's pinnacle, do not seem to have changed his confident but humble attitude.
"Coming from a small fishing village in Panama," Yankees Brian Cashman said, "to the biggest media market in the world, and playing the game of baseball to become the greatest of all time and for as long as he's done it ... he's still the same guy."
The Yankees opened in Cleveland on April 2, 1996, returning home to face the Royals a week later in a game memorably played completely in snow. In his role as the long reliever, Rivera was pitching irregularly as the Yankees hadn't found the formula to best use the promising hurler.
He was throwing hard then, clocking in the mid-90's with his fastball velocity, but the legendary cutter that Rivera calls "a gift from God" hadn't yet appeared. It materialized in his 1997 game of catch with fellow reliever Ramiro Mendoza. Rivera had no way to foresee what was ahead.
"How could you have known?" Rivera said. "All these things, I cannot say I would have imagined."
Here in 2012, Rivera has strongly hinted all spring that he is contemplating leaving the cutter at the ballpark soon. He says that he knows what he will be doing in '13, and that his decision -- which he has shared with his family, plus Jeter, a member of his Yankees family -- is "irrevocable."
There are higher callings ahead for Rivera; he said he would consider instructing young pitchers at the Minor League level someday on a temporary basis -- but his passion is for the church, and he hopes to increase his involvement in that arena.
"I know what I'm going to do after this," Rivera said. "I definitely know what I'm going to do. There's a lot of things more than baseball that I want to do."
Each time Rivera has walked off the mound this spring from his clean innings of work, he has earned standing ovations that seem bittersweet from the outside, as though they are acknowledgements of a reality no one has wanted to accept.
But for Rivera, his anticipation for the season ahead has not changed as the clubhouse at George M. Steinbrenner Field fills with empty cardboard boxes, at least one of which will be stuffed with the personal effects Rivera will need for his workplace at Yankee Stadium.
"It's the same [feeling]," Rivera said. "I appreciate every day. You have to do the work and finish your stuff. We have responsibilities."
The end of spring is near, and Rivera is looking ahead for another reason -- leaving his family behind at his New York-area home has become more difficult with each passing season. But as Rivera considers where he was in 1996, sometimes he doesn't feel all that far removed from the young man who had no idea what was ahead.
"Of course," Rivera said. "You have to have this passion for the game. Otherwise, you won't be here. But being home, there's nothing better than that."