But most of the NFL teams that scouted and evaluated him, including the one that ended up drafting him in the fourth round in 2006, the Jets, had other ideas.
"I was really hoping to play quarterback," Smith said. "That's all I played my whole life. But after I got drafted, coach [Eric] Mangini said just come in and do whatever we ask. At that point, I was scared to death. I wanted to do whatever they said.
"I didn't know what to expect or how long or anything. I just put my head down and worked and did what they told me."
The bad news is the quarterback thing pretty much never got off the ground for Smith. He's thrown just 10 passes in eight NFL seasons.
The good news is he's still managed to carve out a very good 8-years-and-counting career by being a jack of all trades.
Smith can do whatever a coach needs him to do, which during his NFL career has included playing wide receiver, running back and quarterback, as well as all four special teams. He is the only player in NFL history to score touchdowns via rushing, receiving, passing, kickoff return and blocked punt.
Smith's versatility is why the Eagles signed him last November after he negotiated his release from the Buffalo Bills, and why he not only will be on their season-opening roster, but also could be their Week 1 slot receiver.
"When you have someone that's the third receiver or the fourth receiver or whatever, that has that multiplicity in them, it really helps," Eagles coach Chip Kelly said. "I think when you're trying to round out your roster, the versatility really at the bottom of the roster is the key thing.
"When you look at Brad, he's a four-core special-teams guy, and is constantly making tackles on the kickoff-cover team and plays wing or personal protector on the punt team, can return kickoffs and is on our punt-return team, and also can play multiple positions on offense.
"I think it just helps the depth, especially on game day when you only have 46 guys active, to be able to have somebody that can play a lot of different roles and also back up in a lot of different roles."
Smith, 30, played in the Eagles' last six regular-season games, primarily on special teams. He played just 20 offensive snaps and had two receptions as he tried to get up to speed with Kelly's offense. He also had one pass attempt - an incompletion - and averaged 26.5 yards on four kickoff returns.
Smith figured to be the team's fifth wideout this season behind Jeremy Maclin, Riley Cooper and rookies Jordan Matthews and Josh Huff, and also play on all four special teams.
But Maclin and Cooper have missed time this summer with injuries, and Kelly is trying to bring the 6-3, 212-pound Matthews along slowly. So Smith has been getting almost all of the first-team reps in the slot in three-wide receiver personnel packages.
"It's been good to have the whole offseason [to learn the offense] and sit in meetings and talk to position coaches and actually understand the big picture of the offense instead of just trying to learn the game plan from week to week like last year, which was difficult," Smith said.
Matthews, the Eagles' talented second-round pick, likely will be the primary slot receiver at some point this season. Kelly is eager to match him up against smaller nickel corners.
But right now, the job belongs to Smith, who at 6-2 and 213 pounds, is only an inch shorter than Matthews. While Smith may not have Matthews' pass-catching potential, he's a disciplined route-runner and an effective blocker, which is no small thing in an offense that saw the Eagles run the ball 47 percent of the time last season.
"One of my favorite things is blocking," Smith said. "On a punt return or a kickoff or a run. That's what it's about. It's about winning."
Matthews said Smith has been a big help to him in his transition to the pro game.
"The main thing I've learned from Brad is being a professional," he said. "The dude is so consistent. He's the same person day in and day out. You couldn't ask for a better guy to learn from.
"He knows that coming in as a rookie is going to be something that's extremely hard, extremely challenging, and he's always been positive with me. He's always trying to encourage me.
"He quizzes me a lot, making sure I know the plays, know what I have to do on each route and certain things like that. I really couldn't have asked for a better guy to be playing behind right now."
Smith was used as an occasional Wildcat weapon with both the Jets and the Bills. In 2009 with the Jets, he averaged 11.5 yards per carry on 18 rushing attempts. A year later, he averaged 7.9 yards per carry with on 38 carries, including a 53-yard touchdown run. He had two carries for 2 yards in his late-season stint with the Eagles last year.
When the Jets first moved Smith from quarterback to wide receiver his rookie year, he had his doubts.
"One day I'd be the receiver and then we would have this period at the end of practice where I would put on a red [quarterback] jersey," he said. "Or I would have a red jersey on during practice and then take it off when I went to receiver.
"There were many nights when I questioned, what am I doing? Because you're used to having the ball in your hands and being the leader. It really humbles you and makes you appreciate the game and your teammates and what it's all about."
The yearning to get behind center still hasn't completely left him. "Once it's in you, it's hard to get it out," he said. "I love talking to Nick [Foles] and those guys and see what they're thinking."
On Twitter: @Pdomo