But after a stellar performance at the Senior Bowl, the Connecticut defensive lineman might have persuaded some scouts and personnel types into selecting him late in the first round, perhaps as high as No. 28 overall where the Packers currently sit.
"I had a decent week at the Senior Bowl, and I just want to build on that," said Reyes at the NFL Combine in Indianapolis.
The word "decent" is just Reyes being humble. He received rave reviews from observers in Mobile, Ala. in early February.
As good as he performed in the game itself––three tackles and a sack for a loss of seven yards––Reyes had an even better week of practice leading up to the contest.
Practice at the Senior Bowl is just as important as the game, maybe more important, for the players involved. Every drill, every snap of every scrimmage, is performed in front of scouts and general managers representing every NFL team, not to mention the public at large through practices sessions being televised on the NFL Network.
Playing for the North squad, Reyes was able to get a taste of the NFL when he was coached by the staff of the Minnesota Vikings, and he ended up leaving a positive impression.
"Reyes impressed at the Senior Bowl by showing the strength to be a factor on the edge in a 3-4 defense and the girth to handle inside duties if used in a 4-3 set," said Matt Miller, NFL Draft senior writer at Bleacher Report, who was in attendance at Mobile. "Reyes displayed a nice first step, something that caused me to go back and take a second look at his game film.
"Playing against better competition than he faced at UConn, Reyes' all-around game was on par with those players being projected in the early parts of the second round."
There's a fine line between early second round and late first round. But if Reyes is going to go that high, he's going to have to convince teams he can fit in their defensive scheme.
Reyes is confident he can do so, and he thinks his time at Connecticut helped prepare him for whatever system he's drafted into at the next level.
"We'd do a lot of running things out of the 4-3 and on third down we'd blitz out of the 3-4 package," said Reyes. "I was kind of all over the field. I played a lot of positions on the defensive line."
Measuring in at 6-4 and a hair under 300 pounds (299) at the Combine, Reyes would be undersized compared to the unquestioned pair of Packers' starters on the defensive line, B.J. Raji and Ryan Pickett, who are close to 350 pounds.
What the Packers really need, however, is an improved pass rush, something they sorely lacked in 2011 after Cullen Jenkins left in free agency to sign with the Philadelphia Eagles.
They might be willing to overlook sheer size in order to find an athlete good enough to consistently get after the quarterback. Given his background playing positions other than defensive line before college, Reyes definitely fits the category of "athlete."
"You'd be surprised how many defensive linemen or linemen period just played other positions in high school," said Reyes. "I played receiver, tight end and linebacker in high school. It sets you with a good base.
"If you have the type of frame that can put on weight, you can have certain advantages over some guys who weren't. But then again, some people are just naturally gifted, so definitely playing different positions helped with my versatility."
If Reyes wasn't an elite performer in college, he was a consistent one. He had 3.0 tackles for a loss and 1.5 sacks as freshman, 6.0 and 3.0 as a sophomore, 10.0 and 2.5 as a junior and 13.5 and 4.5 as a senior.
His production steadily climbed every year, which hints at room for growth and an even higher ceiling as a professional.
The ideal situation for the Packers would probably be to find the next Jenkins, a player that can play end in their base 3-4 defense and then become a pass-rushing defensive tackle in their nickel package.
And that's just what Reyes might be able to provide.
"Probably that's the whole thing about me, I'm a versatile player," said Reyes. "I could kind of see me anywhere. (NFL teams) like my ability to switch in and out of different positions."