john Fox has stated that he wants the seventh overall selection in the 2015 draft to improve his "cardio" before he returns to action.
It has been speculated that White isn't progressing as well as hoped. Quarterback Jay Cutler said in June that White was battling for the No. 4 receiver role.
He was also cited for failure to wear a seatbelt.
The team has yet to comment on the situation with Hill, who has had a disappointing career. He did not play last season for Carolina after two poor years with the Jets.
Parker is still recovering from foot surgery he underwent two months ago. He will likely need another month to complete his rehab.
Nelson last played for Philadelphia in 2011, but has since occupied a roster spot for Carolina.
Powell, who played at Iowa, was signed as an undrafted rookie free agent.
Linebacker Aaron Lynch (leg), wide receiver DeAndre Smelter (knee) and offensive tackle Trent Brown (unknown injury) were also placed on non-football injury, while center Daniel Kilgore was placed on the physically unable to perform list, recovering from a fractured leg.
Byrd is returning from a season ending knee injury. Colston has a non-disclosed injury.
All four are still on the roster and can be activated at any time before the start of the season.
To make room for Hill on the roster, the Jets parted ways with kicker Andrew Furney.