Graham filed a grievance through the players' union. He contends he should be considered a wide receiver, not a tight end, when the team designated him with the 2014 franchise tag. The difference in salary would be more than $5 million.
Arbitrator Stephen Burbank is conducting the meetings that also involve the NFL Players Association, the NFL's Management Council, and the Saints. No ruling is expected immediately.
The Saints gave Graham the franchise tag for about $7 million as a tight end, the position he has been listed at for his entire four-year career. But he believes because he often is split out away from the tackle, he is a wide receiver. That franchise tag is worth about $12.3 million.
According to an analysis by ESPN Stats and Information, Graham lined up split on 67 percent of his snaps: 45 percent of the time in the slot and 22 percent out wide.
But the Saints note that he made the All-Pro team and the Pro Bowl as a tight end and was drafted as a tight end.
Such disputes are not frequent, but draw lots of attention because they can set a precedent. Baltimore's Terrell Suggs, the 2011 Defensive Player of the Year, argued in 2008 that he should be tagged as an end, not a linebacker. The difference back then was about $800,000.
Suggs wound up signing a new deal with the Ravens, then helped them win the 2012 NFL championship.
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