Reese was the Giants' director of player personnel at the time, and Ernie Accorsi, the team's general manager, was fixated on trading for Eli Manning. If the Giants couldn't swing a deal with the San Diego Chargers for Manning, then they were set to take a quarterback out of Miami of Ohio named Ben Roethlisberger with the fourth overall pick.
"Yeah, he's our guy," Reese recalled about a development that never took place. "Both of them had terrific skill sets and they had the makeup that you want for this position. Some guys have the physical skill set but they don't have the mental makeup.
"Both of those guys had that and [Roethlisberger] was at a different level of competition we thought playing at [Miami of Ohio] than Eli. But we thought he would definitely fit in for us. We didn't have any issues with picking him if it came down to that."
The Giants and Steelers are both perfectly happy with how things ended up. The Giants sent quarterback Philip Rivers (the fourth overall pick), their 2004 third-round pick and their 2005 first- and fifth-round picks to the Chargers for Manning.
Roethlisberger was drafted 11th overall by the Pittsburgh Steelers.
A combined four Super Bowl victories later, Manning and Roethlisberger meet for only the third time in their illustrious careers when the Steelers visit the Giants on Sunday. They have split their previous two head-to-head meetings.
"They've been to three Super Bowls since we were drafted that year, so he's a tremendous player," Manning said. "You always kind of take pride in your draft class and guys who have done well, so you look at Ben and see two championships, played in three Super Bowls, been to some Pro Bowls."
Roethlisberger admits that initially he was keeping up with what Manning was doing to see if he could do better.
"Early on for me, it was more wanting to do better than him," the Steelers QB said. "I don't want to say animosity, but he was the No. 1 pick and I think as a guy that's not picked No. 1 or any time someone is picked ahead of you, you want to beat that guy out.
"But as I've gotten older, it's more neat to see his success, to see him getting two Super Bowls because I think it just adds to the legacy of our draft class and all four quarterbacks -- Matt Schaub, Philip, myself and Eli that were drafted [in 2004]."
Roethlisberger and Manning have quarterbacked four of the past seven Super Bowl winners. Roethlisberger won his first two Super Bowl appearances (XL and XLIII), before losing to Aaron Rodgers and the Green Bay Packers in Super Bowl XLV. Manning has won both of his Super Bowl appearances (XLII and XLVI), taking Super Bowl MVP honors each time.
"Both of them winners," Pittsburgh coach Mike Tomlin said. "Both have been to the big dance and delivered. That's what that position, particularly, is about. Both guys have a keen understanding of that and are motivated by that."
Accorsi and Reese seemed to know that Manning and Roethlisberger had something special coming out of college.
The Giants wanted Manning badly. But they were pretty confident that Roethlisberger would have been a terrific fit as well.
"It was there, and the leadership skills," Reese said of what he remembered about scouting Roethlisberger. "And how everybody talked about him there and watching him play, he was a pretty easy guy to figure out."
Reese added: "We thought he had the skill set to be a franchise quarterback, that is for sure. He has proven that, he's done it. He has got skins on the wall. He was a guy you thought you could win Super Bowls with. We were confident that if the trade didn't go down, we were still going to get an outstanding quarterback regardless."
The Steelers and Giants are two of the most storied franchises in the NFL. They have long, proud traditions that stem from their respective ownerships -- the Rooney and Mara families -- and they are built on a somewhat similar philosophy of stability, tough-minded defenses, tradition and character.
"It is not always flashy," Giants defensive end Justin Tuck said of the similarities between the Steelers and Giants organizations. "It is not always what people want to see. But they are constantly in the mix."
That also sounds like the perfect description for Manning and Roethlisberger. On Sunday, the two 2004 classmates will be on the same field again.
Surely there are many who would like to see them face each other more often, perhaps with something bigger and shinier at stake.
"I think they're still writing the story," Tomlin said of the QBs. "Those guys are at a sweet point in their careers, where they're both experienced and still in their primes. I'm sure they're excited about continuing to write that script."
Roethlisberger is eager to see what people will say years from now about the two quarterbacks the Giants had atop their draft board back in 2004.
"I hope that we can play well enough that one day they talk about us as maybe the best quarterback draft class of all time," Roethlisberger said.