The 27-year-old has become one of the most potent weapons in the NFL as he has caught 41 touchdowns in his four seasons with the Saints along with two 1,000-yard seasons.
Graham was involved in a dispute with the club during the off-season over the designation of his franchise tag, as he wanted to be known as a wide receiver while the Saints classed him as a tight end.
An arbitrary hearing ruled in favour of Sean Payton's side's argument, meaning Graham will play the 2014 season on a salary over just over $7m (£4m), but Brees is hopeful that the two sides can come to a long-term agreement.
"At the end of the day, Jimmy Graham has revolutionised the position," Brees told CanalStreetChronicles.com.
"He's a guy who is so talented at so many things you know and obviously he's a big part of our offense and I hope that they're able to reach a long-term agreement here sooner than later."
Graham recorded 86 receptions for 1,215 yards and 16 touchdowns in the 2013 campaign.