The Saints have designated Graham as their franchise player for 2014, although there is an ongoing dispute as to whether he is a tight end or a wide receiver.
While his team insist he is a tight end, Graham is often lined up as a wideout during offensive plays, and he argues that as a franchised player, he should be due wide receiver wages.
He has filed a grievance against the ruling in order to try to get his franchise-tag salary raised.
However, despite the NFL Players Association providing evidence that Graham plays out of position 67% of the time, the NFL wants to use his personal bio against him to prove that he is in fact a tight end.
Graham's bio reads: "New Orleans Saints Tight End #80. Private Pilot."
The league's argument is that if Graham lists himself as a tight end on a personal account, he can have no complaints about being paid the appropriate wages for that position.
A decision on the matter is expected to be made in the coming days.