NFL Network's Michael Silver reported that the snag between the Jets and Darnold deals with the team being able to recoup money should the player be injured in activities outside of football.
Darnold, who was the No. 3 overall pick of the 2018 NFL Draft, was listed as the team's No. 3 quarterback on the depth chart following last month's minicamp. Veteran Josh McCown is listed as the starter with Teddy Bridgewater as his backup.
The Jets moved up three spots after a blockbuster trade with the Indianapolis Colts to select Darnold, who completed 303 of 480 passes for 4,143 yards and 26 touchdowns with USC last season.
McCown is coming off one of the most productive seasons of his career in 2017. The 39-year-old completed 67.3 percent of his passes and threw a career-high 18 touchdown passes with nine interceptions in 13 games before suffering a broken left hand.
The Jets signed Bridgewater, who missed the entire 2016 season and the start of the 2017 campaign after suffering a torn ACL and dislocated knee in August 2016.
Bridgewater was a Pro Bowl selection in 2015, when he started all 17 games for the Minnesota Vikings and led them to an 11-5 regular-season record before they lost in the first round of the playoffs. He appeared in one game for the Vikings in 2017, throwing two incomplete passes.