Mosley played just two games in his first year with the Jets as he battled a groin injury suffered in the season opener against the Buffalo Bills.
The 27-year-old arrived in New York after signing a five-year, $85-million deal in free agency. He was the 17th overall pick of the 2014 draft by the Baltimore Ravens and spent five seasons with the AFC North club.
Mosley, a four-time Pro Bowler, posted back-to-back 100-tackle seasons in 2017 and 2018 with the Ravens.
He's the second-highest-paid linebacker in terms of average salary in the NFL ($17 million), behind only Seattle Seahawks' Bobby Wagner.
The 4-8 Jets currently have the best rushing defense in the league, allowing 75.2 yards on the ground per game. They will face the Miami Dolphins in Week 14 after having their three-game winning streak snapped by the Cincinnati Bengals last Sunday.