Jimmy Graham could be the answer for a few NFL teams
The Saints obviously want him to be listed as a tight end, but Graham would like to receive wide receiver money.
There's a $5.3 million difference between the tag for those two positions, so Graham's destination could largely depend on that number.
Another factor is that another team could swoop in and offer Graham a better offer. They'd have to give up two first round picks to the Saints if they take Graham, and that could deter a lot of teams, considering the value of first round picks.
Chase Stuart of Football Perspective listed a few teams who could consider signing Graham. These teams all have plenty of cap space, desperately need a stud tight end, have a short win-now window, and would likely have a good record in the next two seasons, so the 1st round pick they give up would be a late first rounder, rather than an early one. Some of them would also specifically benefit from the Saints losing Graham.
The teams in question:
Each of those teams has some cap room. The Jets might not have the best prospects for the next few years, but an offense that features Graham and a few solid free agents around Geno Smith could be pretty solid. The rest of the team could make a huge splash if they were to sign Graham. The Falcons and Panthers in particular would love to see the Saints lose their stud tight end.
If Graham is tagged as a wide receiver, it would be a lot harder for any of these teams to sign him. The money plus the picks might be a little too much for teams to stomach.
But if a team manages to pry him away from the Saints, things could get very interesting.