They can do it by using their strong pass-rush rotation to pressure Brees and finding the right matchup to contain dynamic "move" tight end Jimmy Graham.
This two-pronged approach can help Seattle overcome some key losses in their defensive backfield.
The Seahawks have been dominant defensively this season. They rank second in the NFL in both points and yards allowed.
But the strength of their smothering unit, the fabled "Legion of Boom" secondary, will be depleted. Towering cornerback Brandon Browner is still suffering from a groin injury and now faces a potential one-year suspension for violating the NFL's substance abuse policy.
To compound matters, Browner's replacement, Walter Thurmond has already received a four-game suspension for drug violations. Drug violations have been a major issue for this Seahawks team and the latest suspensions have come at the worst time.
It leaves them with a weakened pass defense against Brees and his fleet of versatile receivers. He can target the likes of wideouts Marques Colston and Lance Moore, as well as running back Darren Sproles.
But the most dangerous pass-catcher at Brees' disposal is undoubtedly Graham. He is a matchup nightmare for defenses thanks to his ability to win against any coverage.
At 6'7" and 265 pounds, Graham is too big for most defensive backs to cover. But he also possesses the vertical speed and athletic range to dominate linebackers.
Clare Farnsworth of Seahawks.com offers some statistics that reveal how Graham causes problems at every level of a defense:
"Graham the ball-control guy has 20 third-down receptions, which ties him for seventh in the league. Graham the big-play guy--the one who can run 40 yards in 4.53 seconds--is averaging more on his other 45 receptions (15.6 yards) than he is those drive-sustaining catches (12.2). He has receptions of 56, 51, 44, and 43 yards. He has at least one touchdown catch in seven of the Saints' 11 games. He has six games with at least 100 receiving yards, including a 179-yard performance. He has two games with 10 receptions and two more with nine."
The Seahawks may have to get creative to corral Graham. That could involve using their best cover man, cornerback Richard Sherman, to shadow him, according to ESPN's Terry Blount.
It is a smart suggestion and echoes a tactic the New England Patriots used against Graham in Week 6. They assigned big cornerback Aqib to aggressively clamp on Graham all over the field.
Sherman is certainly capable of doing the same, but with resources at cornerback stretched, Seahawks head coach Pete Carroll might turn to one of his star safeties for help.
Both Kam Chancellor and Earl Thomas have the size and tenacity to lock up Graham in press coverage. The Seahawks aren't afraid to play with only one deep safety and even show some Cover 0 looks.
So they can afford to dedicate a safety to underneath coverage. Regularly matching up Chancellor over Graham would be Seattle's best bet.
He has the size at 6'3" and 232 pounds to rough Graham up in press man coverage. That would leave Thomas to help out Browner's replacement, while Sherman locks down his receiver one-on-one.
Chancellor is already relishing his battle with Graham, according to The News Tribune's Todd Dybas: " Big tight end, big safety; it's going to be a good matchup."
Of course, the best way to stifle Graham would be getting to the man who throws him the ball. Pressuring Brees will be an obvious priority for the Seahawks and they have an array of weapons to do it.
In particular, Carroll could lean on a pass-rush package featuring a four-man line comprised of a quartet of outside pass-rushers. Hybrid playmakers Chris Clemons and Bruce Irvin man the edges, while defensive ends Cliff Avril and Michael Bennett move inside.
Carroll often relies on this front in obvious passing situations, but could risk it more often to get to Brees.
It would give the Seahawks a better chance of creating pressure with just a four-man rush and protecting their weakened secondary. This is something The Seattle Times' Javson Jenks believes could prove crucial against the Saints second-ranked passing attack.
Even with their losses in the secondary, the Seahawks have the defensive resources to frustrate Brees and the Saints.
Bennett and Avril have given them a stronger pass-rush rotation, so they should be able to consistently pressure the pocket.
If Chancellor is able to keep Graham quiet, Seattle can edge a close one on Monday night.
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