With the Jimmy Graham grievance hearing completed and the outcome now in the hands of an arbitrator, some league insiders believe that the NFL wants to see the player and the team take a page from Terrell Suggs and the Ravens, circa 2008.

Six years ago, Ravens G.M. Ozzie Newsome and agent Gary Wichard (who died in 2011) resolved among themselves the question of whether Suggs is a linebacker or a defensive end for purposes of the franchise tag. While the Saints have done a very effective job of creating the impression that they have nothing to do with the position that Graham’s position for franchise-tag purposes should be tight end not receiver, the reality is that the Saints have plenty to gain — and plenty to lose — based on the outcome. With $5.3 million in cash and cap space hinging on the question of whether Graham is a tight end or a receiver for tag purposes, the Saints undoubtedly want the number to be lower. Especially since the $12.3 million receiver tag would lay the foundation for a far pricier long-term deal.

With Suggs, the two sides worked out a one-year franchise tender and then struck a long-term deal in 2009. With Graham, the best outcome for everyone would be a long-term deal forged during this period of uncertainty regarding the outcome of the grievance.

Of course, that would require the Saints to deviate from their apparent preference to work out a new deal on the latest possible date. In this case, the deadline for a long-term deal arrives on July 15.

The Saints pushed it to the limit two years ago with Drew Brees, losing along the way a grievance that seemed far more winnable than the current one. Brees argued that, if the Saints (who applied the franchise tag in 2012) were to tag him again in 2013, he’d be entitled not to a 20-percent raise but a whopping 44-percent raise, since it would be the third time in his career that Brees drew the franchise tag. (The Chargers tagged him in 2005.) The argument seemed weak and flimsy and unsupported by the plain language of the labor deal. And yet Brees still won.