Graham was tagged by the team in March. The designation this year for tight ends is $7.035 million.
Graham then filed a grievance through the National Football League Players Association last week, hoping to be designated as a receiver instead of a tight end. The franchise tag salary for a wide receiver is $12.3 million.
A two-time Pro Bowler, Graham lined up at receiver more than two-thirds of the time last season.
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Saints general manager Mickey Loomis declined to answer specific questions about the pending debate over the weekend, but he did say the Saints' side of the argument will be handled by the management council.
"Obviously we get consulted and talked with," Loomis said. "But that's the management council's duty."
Graham caught 86 passes for 1,215 yards with a league-leading 16 touchdowns last season for the Saints. BURKE & FARRAR: 2014 NFL draft grades: Vikings, Packers and Raiders receive highest marks