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.
They can be activated at any time during camp, but must be back in action for the opener or they will be forced to miss the first six regular season games.
The team has not revealed the nuture of the problem, but it arose during activities off the field.
Johnson did miss some time this offseason with a back injury.
Dennard, who was waived by the Patriots in mid-May before his pick-up by Arizona, played in 29 games for New England over the past three seasons.
Gresham underwent back surgery in July. If he is not ready to play by the start of the regular season, he will lose six games.
Kerrigan, who is rehabbing from a knee injury, has averaged 62 tackles over four seasons with Washington and compiled a career-high 13.5 sacks in 2014.
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.
Chancellor, who us already the league's seventh-highest paid safety at $7 million a year, wants more guaranteed money added to his deal. He signed a four-year extension with Seattle two years ago.
Chancellor recorded 78 tackles, an interception and a forced fumble in 14 games for the Seahawks last season.
Nelson last played for Philadelphia in 2011, but has since occupied a roster spot for Carolina.