With 412 career tackles, 45.5 sacks, 42 defended passes and 14 forced fumbles, 32-year-old Brown would strengthen any team's defensive end corps.
Here are five NFL squads that should ink Brown to a contract.
The New York Giants have been having needless drama this training camp with disgruntled star defensive end Osi Umenyiora missing two weeks of practice over a contract dispute.
Despite Umenyiora going back to practice, he then gets injured and has to undergo arthroscopic surgery on his right knee, making him miss four to six weeks.
With rookie end Jason Pierre-Paul having occasional back problems, coupled with Umenyiora's unreliable commit and injury, Alex Brown could be a starter or invaluable backup, helping alleviate the Giants' pass rushing problems.
The Atlanta Falcons' pass rush has had some difficulties this 2011 preseason, as evidenced from the Pittsburgh Steelers' game.
It's true the secondary allowed those yards, but the Falcons' defensive line and linebackers haven't been pressuring the opposing quarterback well.
Alex Brown is a good at pressuring the quarterback, averaging five sacks a season and multiple quarterback pressures. He could be a solid backup for John Abraham and Ray Edwards, bolstering the end rotation.
This move would make sense for Alex Brown and the Chicago Bears.
Brown played is initial eight seasons with Chicago before leaving in 2010 for New Orleans.
He was named Sports Illustrated All-Pro in 2005 for having 45 tackles, six sacks and three forced fumbles for the Bears and was a first and second alternate for the 2005 and 2006 Pro Bowls.
Brown was instrumental in the 2005 and 2006 Bears' playoff runs and started 107 games at end during his Chicago tenure.
The Bears could use another solid backup to replace released defensive end Vernon Gholston, whom they released yesterday. Brown could also ably fill in for starters Julius Peppers and Israel Idonije when they need a breather and provides extra insurance if one of them is injured.
The Oakland Raiders have been hurting for years with their run defense, having been at the bottom part of rush defense categories since their 2002 Super Bowl run.
Alex Brown is a solid run stopper who has the ability to get off an offensive tackle's block to bring down the running back on the outside.
With the Raiders already having top ends in Matt Shaughnessy and Lamarr Houston and an excellent tackle in Richard Seymour, Brown would be a good backup who would make Oakland's front four something to constantly worry about every play.
The Minnesota Vikings have always had a strong defensive line with end Jared Allen and defensive tackle Kevin Williams.
However, the Vikings lost defensive tackle Pat Williams to free agency, and starting left end Brian Robison is not that strong of a player (he had 15 tackles and two sacks last season).
Alex Brown, even though he is four years Robison's senior, could replace Robison at left end as he had 39 tackles, two sacks and a forced fumble last year for the Saints.
Bob Bajek is a freelance reporter and can be followed on Twitter.