A 6-foot senior, Burrell had 41 tackles last season as he started every game.
The Vols, who travel to LSU on Saturday, rank last in the SEC in passing yards per game allowed (309.3).
Heupel also confirmed that standout wide receiver Cedric Tillman had surgery on his ankle.
Heupel said Tillman had the tightrope procedure in order to expedite his recovery.
"He was limited," Heupel said, "but moving around a little bit today. We'll continue to see how it unfolds this week and see where we're at."
Tillman has 17 catches for 246 yards in his first three games.