According to Yahoo! Sports, Jimmy Graham could seek up to $12 million annually on his next contract.
The Saints and Jimmy Graham have yet to hold talks about a contract extension, and there is "no indication" they will.
Jimmy Graham confirmed that "everything's going well" with his recovery from wrist surgery.
Jimmy Graham triggered an escalator in his rookie deal, raising his 2013 salary from $575,000 to $1.323 million.
Jimmy Graham has opted out of the Pro Bowl after undergoing wrist surgery earlier this month.
Jimmy Graham dropped 15 of 100 catchable passes in 2012.
The Times-Picayune says it appears Jimmy Graham is in "prime position" to ask for a new contract.
Jimmy Graham caught nine passes for 115 yards with one touchdown in the Saints' Week 17 loss to the Panthers.
Jimmy Graham (wrist) is on the Week 17 injury report, but practicing in full.
Jimmy Graham leads the league in drops this season with 13.
Jimmy Graham played through a dislocated right ring finger in Sunday's overtime win over the Cowboys.
Jimmy Graham caught seven passes for 88 yards in Sunday's Week 16 overtime win over the Cowboys.
Jimmy Graham is listed on the Week 16 injury report with a wrist issue, but is practicing in full.
Jimmy Graham caught five passes for a team-high 69 yards in New Orleans' Week 15 win over the Bucs.