For New Orleans Saints tight end Jimmy Graham, a game in which he broke a team record for touchdowns by a player at his position was good enough to earn him recognition as the best man on offense in the NFC this week.

The NFL named Graham the NFC Offensive Player of the Week on Wednesday after he caught nine passes for 134 yards and two touchdowns in a 31-7 blowout of the Arizona Cardinals on Sunday at the Mercedes-Benz Superdome. The two scores brought his career total to 29 and made him the all-time franchise leader in touchdown receptions by a tight end, surpassing the 27 that Henry Childs hauled in for the Saints between 1974 and 1980.

Graham’s effort on Sunday followed a team record-setting 10-catch, 179-yard and one-touchdown performance in a 16-14 win at Tampa Bay in Week 2 for the Saints. He finished Sunday with the most yards by a tight end in a two-game span since Shannon Sharpe gained 314 yards in consecutive contests in 1996 for the Denver Broncos.

After Arizona’s defeat to New Orleans, Cardinals’ Pro Bowl cornerback Patrick Peterson said this about Graham: “All that Drew (Brees) ... has to do is pretty much throw it in his vicinity and he is pretty much going to come down with it.”

Graham’s player of the week honor is the second of his career, and the NFL said he joins Shannon Sharpe and Alge Crumpler as the only tight ends to win the award more than once. Graham’s first one came after he caught seven passes for 146 yards and two touchdowns in Week 10 last year, when the Saints beat the Atlanta Falcons 31-27 at the Superdome.

In that game versus the Falcons, Graham set a record for yardage by a Saints tight end in a single game, which he then shattered against the Bucs this year.

Graham landed his latest player of the week laurel while reports circulate that the star tight end has been offered a new contract by the Saints. Now in the final season of his rookie deal, Graham has amassed 358 receiving yards, 23 receptions and four touchdowns.

He’s by far quarterback Drew Brees’ favorite target and stands among the biggest reasons the Saints are 3-0, their best start since winning Super Bowl XLIV four seasons ago.

Graham has not responded to the contract offer, according to a Pro Football Talk report citing anonymous sources. Many expect Graham to become the best-paid tight end in league history and believe he is worthy of a contract of $10 million or more annually.

The Saints selected the 6-foot-5, 265-pound Graham in the third round of the 2010 draft. He went to the Pro Bowl in his second season.