In a letter released by the rapper J Cole on Instagram, Kaepernick - who addresses Jets general manager Joe Douglas - says he would be "honored" to join the team and "lead the practice squad" with "the sole mission of getting your defense ready each week."
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Following Aaron Rodgers' season-ending Achilles injury in the team's opening game of the year, the Jets - who lost to the New England Patriots on Sunday to drop to 1-2 on the year - have been forced to turn to Zach Wilson as their starting quarterback, who has floundered in the position.
"I am sure of my ability to provide you with an elite QB option if, God forbid, QB1 goes down," Kaepernick wrote. "However, I know that there may naturally be uncertainties from you and possibly from others about my playing abilities.
"This plan, I believe, allows me to be of great service to the team as a practice squad QB, while also giving you a low-commitment chance to assess my capabilities to help in any other capacity you may see fit.
"Worst case scenario, you see what I have to offer and you're not that impressed. Best case scenario, you realize you have a real weapon at your disposal in the event you ever need to use it. In either of these scenarios, I would be committed to getting your defense ready week in and week out, all season long, and I would wear that responsibility like a badge of honor."
Wilson, the former No. 2 overall pick in 2021, has struggled in his two seasons since joining the Jets, a key reason for Rodgers' acquisition in the offseason.
And since being thrust back into the starting line-up, Wilson has continued to show why he was benched in favor of Rodgers. Although he was able to lead the team to an opening week victory over the Buffalo Bills, the Jets have since gone on to lose to the Dallas Cowboys and the Patriots with Wilson looking scrambled and out of sorts.
It has led to calls for the team to look at other options at quarterback with Joe Namath, the only quarterback to win a Super Bowl with the Jets, becoming the latest to call for the team to make a change.
"I wouldn't keep him," Namath said on The Michael Kay Show on 98.7 ESPN New York. "I've seen enough of Zach Wilson. All right? I've seen enough."
The Jets addressed those calls somewhat by signing veteran quarterback Trevor Siemian to the practice squad on Tuesday to add depth at the position.
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The questions surrounding Wilson's permanency at the helm of a team with playoff aspirations continue to swirl though and the void is something that Kaepernick says he is willing to help address.
The 35-year-old explained that if he was signed to the practice squad, he would be able to provide the team's defense with a better opportunity to prepare against a mobile quarterback and allow team executives to be able to evaluate Kaepernick's ability without putting pressure on Wilson.
Kaepernick hasn't played in the NFL since 2016 after his refusal to stand for the national anthem ahead of games to protest police brutality and racial injustice while he was with the San Francisco 49ers sparked controversy.
In March 2017, Kaepernick opted out of his 49ers contract and became a free agent, but no NFL team signed him. In October 2017, he filed a grievance case against the NFL, alleging that teams were colluding to deny him a job. The quarterback settled the grievance with the NFL in 2019.
He addressed the question about his long absence from the NFL in the letter, saying that he has remained ready.
"Unlike many of the veteran QB's that have been named in the media, I've never retired or stopped training. My training schedule has remained the same for 6 years; Monday through Friday, 5am-8am training on the field and in the weight room. I've kept this training schedule without failure for the past 6 years, in hopes that an opportunity will present itself."
In his letter, Kaepernick also provided references for Douglas, including two of his former 49ers head coaches, Jim Harbaugh and Chip Kelly, and Las Vegas Raiders owner Mark Davis.
'We need to grow up a little bit'
While he's not able to help on the field, Rodgers is trying to play his part by being a calming influence on the rest of the Jets team as one of the veterans in the locker room.
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The 39-year-old said on "The Pat McAfee Show" on Tuesday that he would like to see the whole team "take a couple of breaths," while also calling for more unity as a whole.
"I think too many little side conversations and we need to grow up a little bit on offense, lock in and do our job - everybody - and not point fingers at each other and that's everybody," the four-time NFL MVP said.
"Don't point fingers at the coaching staff, don't point fingers at each other, just get back to work and get the job done."
Rodgers added: "It's more of the side stuff that I don't like. I want to see us stick together through the tough times.
"I said it to them in the preseason. Our toughest task is how we handle success. That's whether we're having success or not have success that doesn't mean we're winning all the time; you have to handle it the right way. It's when we're not having success, how do we respond? How do we respond to adversity? And that goes to our fan base and former players as well. You're not helping the cause."
The Jets' schedule doesn't ease up though as they host the reigning champion Kansas City Chiefs on Sunday night.
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