The expected move, first reported by the NFL Network, will make Pryor, a first-round pick in 2014, a free agent after the 2017 season.
The Jets waited until after the draft before determining their plan for Pryor because they wanted to see whether they picked a safety in the draft.
New York may continue efforts to trade Pryor, although team officials suggested there is no urgency to move the 24-year-old. He is counting only $2.7 million ($1.6 million guaranteed) against this year's salary cap, and coach Todd Bowles said he can use Pryor in three-safety packages with the two rookies.
Pryor has been inconsistent in three seasons as a starter. In 44 games, he produced only two interceptions, two forced fumbles and a half-sack under two coaching staffs.
The fifth-year option would have been $5.266 million in salary for 2018, guaranteed for injury only.