The New Orleans Saints and star tight end Jimmy Graham are on the verge of hammering out a new contract, according to ESPN.

Graham would become the highest-paid tight end in NFL history.

The Saints and Graham are facing a 4 p.m. Tuesday NFL deadline to avoid having him play the entire season under a $7.053 million franchise tender.

Graham appealed the arbitration case he lost, but that's regarded as a procedural formality.

If he gets the new deal, Graham is expected to drop teh appeal.

During the past three seasons, Graham has averaged 90 catches, 1,169 yards and a dozen touchdowns per year.

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Aaron Wilson covers the Ravens for The Baltimore Sun