Graham addressed recent comments made by Saints general manager Mickey Loomis, who acknowledged that he would prefer to reach a long-term deal with the star tight end but said New Orleans would use its franchise tag on the Pro Bowler if necessary.
"I'm not keen on the franchise tag," Graham said after Pro Bowl practice Friday, according to NFL.com. "That would be really unfortunate, but that is really all I have to say about that one."
Graham, who led the NFL with 16 touchdown catches this past season, said he would prefer not playing 2014 on the one-year franchise deal.
"That's real unfortunate," he said. "If that happens, it doesn't really matter what I prefer."
If New Orleans uses its franchise tag on Graham, the move likely would trigger a groundbreaking battle over whether the pending free agent should be officially considered a tight end or a wide receiver.
Loomis, who has stressed that the March 3 franchise-tag deadline is more than a month away, also made it clear that the Saints consider Graham a tight end.
"Isn't that what we drafted him as? Isn't that what he made the Pro Bowl as?" Loomis said Tuesday. "That's what we see him as, a tight end. ... That's what makes him valuable."
The difference between the franchise-tag salary for a receiver and a tight end will be significant. Last year it was $10.5 million versus $6 million.
According to ESPN Stats & Information, Graham lined up as a receiver on 67 percent of his snaps in 2013 (45 percent in the slot, 22 percent out wide, 33 percent as an in-line tight end).
During his four-year career with the Saints, Graham has 301 receptions for 3,863 yards and 41 touchdowns.
ESPN.com Saints reporter Mike Triplett contributed to this report.