Session was not on the field for the team's two practices Friday because he is still dealing with post-concussion symptoms, coach Mike Mularkey said.
"It's definitely a concern," Mularkey added.
Session had at least two concussions last year, one in the preseason and another against Cleveland on Nov. 20. He was placed on injured reserve two days later and missed most of the team's offseason workouts.
The team had hoped he would be ready for camp, but Mularkey said setbacks have slowed his progress.
"It's kind of been an up-and-down process," Mularkey said. "You just kind of get your hopes up and he'll have something that will set him back."
The former Indianapolis Colts starter signed a five-year, $29 million contract with Jacksonville last year. The deal included $11.5 million guaranteed. The Jaguars paid Session a $2.25 million roster bonus in March, but Mularkey wasn't sure when or if he will play again.
"We just don't know the future with him," Mularkey said.
Versatile backup Russell Allen will assume Session's spot in the lineup.
"It's definitely what we all strive for, but by no means did I ever want to get it this way," Allen said. "I don't know much about his situation. All I was told is he's not ready to play right now. I'm acting as the guy until he's back. That's been my role all along: filling in for guys when they're not healthy. As of today, he's not."
Session attended some organized team activities in May and even did some light running on the field. It's unclear when he experienced post-concussion symptoms or the severity of them.
Session has 308 tackles, six forced fumbles and 2½ sacks in five seasons. He missed 11 games in 2010 because of an elbow injury, and also had other nagging injuries in his first season with the Jags.
His concussions, though, could be career threatening.
"I'm not going to give a timetable," Mularkey said. "Clint is still having some problems with some concussion symptoms. We're trying to make sure we do that correctly, especially with the history of the concussions that are going on lately. We're dealing with Clint. We're going to not push him into anything. ... I think we're more aware of a lot of things today, especially with the concussions and the tests you're allowed to administer. Everybody's much more aware of what's going on with them."
The Jaguars ranked sixth in the league last year in total defense, thanks partly to a revamped linebackers corps that included Session and Paul Posluszny. Jacksonville signed both to lucrative free-agent deals to play alongside veteran Daryl Smith.
Now, Session is on the physically unable to perform list with guard Uche Nwaneri, defensive tackle Terrance Knighton, defensive end John Chick, tight end Zach Miller and offensive tackle Cameron Bradfield. The Jaguars expect most of them to be on the field and practicing full speed soon. They have no idea about Session, though.
In the meantime, Allen will try to make the most of his opportunity.
"When you walk in the door, you want to be a starter," Allen said. "I wouldn't be sitting here today if I didn't want to be the best and if I didn't want to compete. That's not how you ever want to get (a starting job). You don't want to wish that on anyone."