But Brees did not fall on either side of the debate this time, taking a more diplomatic approach when evaluating Graham's position in a recent interview with the ESPN Radio's "The Dan Le Batard Show."
"He's a hybrid," Brees said during the interview, which took place Thursday night. "I don't know if there's anybody like him or ever like him."
Brees' statement differed from his remarks earlier this offseason. In an interview with NBC Sports Radio in January, Brees described Graham as a tight end on multiple occasions.
The Saints placed their franchise tag on Graham earlier this month, tendering a $7.04 million offer to the two-time Pro Bowler. Barring a holdout, Graham will play the 2014 season under the distinction of tight end rather than wide receiver.
The 6-foot-7, 260-pound Graham could still opt to file a grievance, asking to be designated instead as a wide receiver, which carries a $12.3 million franchise tag. Graham's camp is believed to be seeking a long-term contract that is more in line with the NFL's top receivers than the league's top tight ends.
The Saints have remained adamant throughout the process that Graham is a tight end, but Brees doesn't necessarily see it that way.
"He plays a different position than anybody in the league," Brees said during his interview with ESPN Radio. "So he'll be cutting edge with whatever he gets [paid]. And everybody will try to compare themselves to him five years from now."
Graham and his agent, Jimmy Sexton, likely will file a grievance through the players' association, asking that Graham be considered a receiver because he lined up out wide or in the slot on 67 percent of his snaps last season.
It's a significant distinction, and a favorable ruling would give one side serious leverage in long-term contract negotiations.
"He's a little bit of everything," Brees said. "He can do it all. Obviously he takes a lot of snaps in a two-point stance, off the ball, split outside, by himself. We move him all over the place."
Graham had 86 catches for 1,215 yards and a league-leading 16 touchdowns last season, his fourth with the Saints.
ESPN.com Saints reporter Mike Triplett contributed to this report.