However, much to his surprise, he was very much in demand this offseason. Alexander weighed numerous offers and decided that New York, with incoming defensive coordinator Tim Lewis, was definitely the place to be.
"I talked to quite a few teams, but the scheme I was going to play in was important to me," said the 33-year-old Alexander. "Staying in the same scheme allows me to play faster".
"This was probably the best situation for me."
Indeed it was because Alexander, 5-11, 200, spent his previous four seasons in Pittsburgh, where Lewis, known for his player-friendly, aggressive, attack-style defense, was in charge.
Alexander was the defensive quarterback in Pittsburgh, never missing a game and posting between 79 and 92 tackles every season and intercepting a career-high four passes in each of the last three years.
Tom Coughlin noticed Alexander's veteran savvy ways during the offseason minicamps.
"Twice he's acted as if he was going toward the hash (mark) only to turn his back and lure the quarterback into making a throw his way," Coughlin said. "He's done a few things to show that he has a great grasp of the mental part of the game."
Alexander, who was released by the Steelers in March, knows very well it was his mind, not so much his feet, which kept him around as long as he's been.
"I have to play smart, that's the biggest key to being a free safety," he said. "You have to keep everything in front of you, be a sure tackler and be patient."
Patience was certainly a virtue for Alexander, who turned down several athletic scholarship offers and attended Tennessee State on a prestigious presidential academic scholarship to study computer science. According to Alexander, the only reason he played football was as a show of thanks to coach Joe Gilliam, Sr., who wrote him a strong letter of recommendation.
Boy was that ever a wise career move. Alexander said that once he realized he still had a chance to continue toiling in the NFL after 10 seasons, he didn't have much of a decision to make.
"I guess I came close to retiring but you always have to realize that the NFL is one of the greatest opportunities of your life and you don't want to pass that up," he said.
The soft-spoken, humble Alexander said he takes no special pride in having played in every game for six straight seasons, 110 contests in a row to be exact. Alexander comes to the Giants with 863 career tackles (576 solo), 30 special teams tackles, 21 interceptions, 4.5 sacks, 11 forced fumbles and four fumble recoveries. Last season with the Steelers, Alexander finished with 83 tackles (61 solo), five special teams tackles, four interceptions, two forced fumbles and two fumble recoveries.
The shining moment of Alexander's career came when he picked off two passes for the Steelers in a playoff win over Baltimore in 2001.
Before joining Pittsburgh, Alexander spent four seasons in Arizona, where he was signed as an undrafted free agent, and two campaigns in Carolina, where he posted a career high with 114 tackles in 1998.
Now he looks for even bigger and better things with Big Blue. He finds himself in a stiff battle for the starting free safety spot with incumbent Omar Stoutmire. One surefire way to gain an edge is by picking the ball off during camp. New York has set team record lows in INTs the last two seasons, posting an abysmal total of 10 picks in 2003.
Coughlin said that Alexander's experience playing for Lewis could go a long way toward landing number 26 in the starting lineup.
"He has a lot of an advantage," Coughlin said. "There are so many subtleties and so many teaching points and coaching points. When you get into the third down stuff and there are all kinds of situations. All of those things result in small detailed changes in coverage. Brent has been through that; he's listened to that and he really can be a big help on the field with the other players because he's knowledgeable."
Secondary mate Will Allen has certainly noticed.
"One of the main things he brings is that he knows this system," he said. "I can tell you there's a big difference for me when I line up now as opposed to when I lined up totally knowing the system; there's a total difference. It really cuts down on the wasted movement that you have. Just the fact that he knows the system is a definite plus. He's an old vet, he's been around a long time and he's a smart player. He's a good player."
In typical Alexander fashion he said he would like to start, but that it wasn't that important to him.
"At this point in my career, I've seen too much that I just want to be on the field and making plays," he said. "I'm not going to get down on myself or anything if I'm not the starter. I'm just going to play the way I play and let the chips fall where they may."
"Everyone wants to start. But with the way the league is, you just want to fit in and be a part of the package. Getting on the field is the most important thing to me."
Free as a bird
The Giants Beat Top Stories
Giants Top 3 Offseason NeedsThe New York Giants have a legitimate chance to represent the NFC in Super Bowl LII next February, but to do so they need to fix some major concerns in all facets of their game. …
The Giants Beat02/10/2017
Giants Early-Mock Draft: First RoundThe Giants Beat scout's who Big Blue should take with its top draft choice in 2017.
The Giants Beat02/08/2017
Giants still only team to beat Brady in SBEli Manning and Big Blue now have another claim to fame following Sunday's win by the Patriots.
The Giants Beat02/06/2017
Top 5 Moments: Giants 2016 Season RecapThe Giants Beat takes a look back at the defining five moments of Big Blue's 11-5 campaign.
The Giants Beat02/06/2017