Mosley, 28, became one of the NFL's highest-paid inside linebackers when he inked a five-year, $85-million contract with the Jets in free agency in March 2019.
But the four-time Pro Bowler suffered a groin injury in Week 1 and was sidelined through 14 games last season. In two appearances, Mosley racked up nine tackles, one pick-6, and two pass breakups.
Mosley's absence would deal a second major blow to the Jets' defense after the team dealt safety Jamal Adams to the Seattle Seahawks in a blockbuster trade last week.
The Alabama product would also be the second Jets player to forgo the coming campaign after offensive lineman Leo Koloamatangi informed New York last week he will sit out.
Selected 17th overall in the 2014 NFL Draft, Mosley spent his first five pro campaigns with the Baltimore Ravens.