A member of the NFL 2010s All-Decade Team, Jordan is an eight-time Pro Bowler, a three-time All-Pro selection, and is the Saints' all-time franchise sack leader.

[5][6] On January 29, 2011, Jordan played in the 2011 Senior Bowl and was part of Marvin Lewis's North team that lost 24–10 to the South.

"[9] On March 9, 2011, he participated at California's pro day, but opted to stand on his combine numbers and only performed defensive end drills.

[15] Jordan was the fifth defensive end drafted in 2011, behind J. J. Watt, Robert Quinn, Ryan Kerrigan, and Adrian Clayborn.

[18][19] Jordan entered training camp slated as a starter, but saw competition for his job after the Saints signed veteran free agent Turk McBride.

Jordan made his first career tackle on running back Ryan Grant and ended a four-yard rush on the opening drive.

[23] On October 16, 2011, Jordan collected a season-high six combined tackles in the Saints' 26–20 loss at the Tampa Bay Buccaneers in Week 6.

[24] On January 1, 2012, Jordan recorded three combined tackles and made his first career sack during a 45–17 win against the Carolina Panthers in Week 17.

Jordan sacked quarterback Cam Newton for a five-yard loss in the second quarter, but was penalized for a horse collar tackle.

[25] Jordan finished his rookie season in 2011 with 31 combined tackles (18 solo), four pass deflections, and a sack in 16 games and 15 starts.

[27] On January 7, 2012, Jordan appeared in his first career playoff game and made one tackle in the Saints' 45–28 victory against the Detroit Lions in the Wild Card Round.

[29] Defensive coordinator Gregg Williams was not re-signed after the 2011 season and was replaced by former St. Louis Rams' head coach Steve Spagnuolo.

[30] Jordan started in the Saints' season-opener against the Washington Redskins and collected a season-high 11 combined tackles (six solo) in their 40–32 loss.

[31] In Week 9, Jordan made seven combined tackles and a season-high three sacks on quarterback Michael Vick during a 28–13 victory against the Philadelphia Eagles.

[34] Head coach Sean Payton was suspended for the entire season due to the New Orleans Saints bounty scandal.

[43] The Saints finished second in the National Football Conference (NFC) South with an 11–5 record and earned a Wild Card berth.

On January 4, 2014, Jordan made four combined tackles and had 1.5 sacks on quarterback Nick Foles in the Saints' 26–24 victory at the Eagles in the NFC Wild Card Round.

[46] Head coach Sean Payton retained Jordan, Akiem Hicks, and Brodrick Bunkley as the starting defensive line in 2014.

[47] In Week 8, Jordan recorded three combined tackles and made a season-high two sacks on quarterback Aaron Rodgers during a 44–23 win against the Packers.

Jordan intercepted a pass by Steelers' quarterback Ben Roethlisberger, that was originally intended for wide receiver Markus Wheaton, and returned it for a six-yard gain in the third quarter.

[49] In Week 17, he collected a season-high six combined tackles and made 1.5 sacks on quarterback Josh McCown in the Saints' 23–20 victory at the Buccaneers.

[57][58] On January 26, 2016, the Saints announced that Jordan had been selected to play in the 2016 Pro Bowl as an injury replacement for New England Patriots' defensive end Chandler Jones.

[66] On September 11, 2017, Jordan made four combined tackles, a pass deflection, and a sack in the Saints' 29–19 loss at the Minnesota Vikings.

[69] Jordan intercepted a pass by quarterback Matthew Stafford, that was originally intended for tight end Eric Ebron, and scored a touchdown in the fourth quarter.

[73] He started all 16 games and made 62 combined tackles (48 solo), a career-high 13 sacks, 11 pass deflections, two forced fumbles, an interception, and a touchdown.

[84] In Week 13 against the Dallas Cowboys on Thursday Night Football, Jordan recorded a season high 7 tackles and sacked Dak Prescott twice.

However, video replay revealed that Jordan forced a fumble, but his return for a touchdown did not count since the play had already been blown dead.

[97] In Week 13 against the Falcons on Thanksgiving Day, Jordan recorded a season high 6 tackles and sacked Matt Ryan 4 times in the 26–18 win.

[99] Jordan finished the season with 52 combined tackles (38 solo), a career high 15.5 sacks, one fumble recovery, and three pass deflections in 16 games started.

[100] In the Wild Card Round of the playoffs against the Vikings, Jordan recorded three tackles and sacked Kirk Cousins once during the 26–20 overtime loss.