OXNARD, Calif. -- Dallas Cowboys linebacker Jaylon Smith wants to play in Thursday's Hall of Fame Game against the Arizona Cardinals, but owner and general manager Jerry Jones said it is unlikely the 2016 second-round pick will.

"I don't know if I'm going to play or not," Smith said. "It's a matter of if they'll let me. Whenever they'll tell me I can go play, I'll go play. I'll just take it day by day. That's what we've been doing. Really looking forward to getting some reps."

Tuesday marked the fourth time in six full-padded practices in which Smith has participated. He took part in eight plays in short-yardage and goal-line situations, stopping Darren McFadden at one point.

"You're seeing the progression and there's no question he's getting better every time he goes out," Jones said.

Jones said Smith is "doing a lot of things out here without the brace at all." He has worn the foot brace in the padded practices. He was not in the brace Monday but he ran without any issues.

"I've been able to do a lot of things without the brace and that'll continue," Smith said.

While he likely won't play Thursday, he will play at some point during the season and that is more than what many people thought possible because of the severity of the knee injury he suffered at Notre Dame.

When asked if he is doing more than he even thought at the start of camp, Smith said no. In a strange way, Smith has enjoyed being sore after practice.

"I experienced that after my first full pads day with contact," Smith said. "It was a great feeling, a reminder of how great and brutal this sport is. I'm very thankful to be out here."

When the Cowboys return to Oxnard on Monday, Smith will continue to be monitored as he works back, but the confidence is growing.

"Just the overall improvement of the comfort of the game, the speed of the game, I've really gotten that down," Smith said. "Now it's about getting reps. The more reps I get, the more comfortable I'll get. Everything is going to be smooth."