The sixth-round pick in 2018 is the second player to file a grievance against the Jets over the past three weeks.
Falk, who started two games for the team while Sam Darnold was out with mononucleosis, is reportedly suffering from a hip injury that requires surgery.
The signal-caller was released on Oct. 12 after Darnold was cleared to return. Falk wasn't listed on the injury report prior to his final start for the Jets or during the week before his release, according to Mehta.
The 30-year-old was released on Oct. 26, the day after independently scheduling a surgery the team didn't authorize.
The Jets and the veteran offensive lineman disagreed over the severity of the shoulder issue. The franchise fined Osemele nearly $580,000 for detrimental conduct, and he filed a grievance to recoup lost wages.
Osemele is also reportedly considering taking action against the Jets' team doctor for violating state medical board regulations.