Tillman missed the Vols' matchup against Florida this past weekend after suffering a high ankle sprain in the team's 63-6 win over Akron in Week 3. He had 17 catches for 246 yards in his first three games.
The No. 8 Vols are off this week. They visit LSU on Oct. 8, and then host Alabama on Oct. 15.
Coach Josh Heupel was not asked specifically if Tillman had surgery when he spoke to the media Wednesday.
"Obviously, we're a long way away from game time," Heupel said of the fifth-year senior's status for the LSU game. "We're hopeful that he will continue to make progress and be available when we go down there."
The tightrope surgery is the same procedure quarterback Tua Tagovailoa had twice while at Alabama. It uses a high strength suture (surgical thread) instead of traditional metal screws. Technically known as the Knotless Syndesmosis TightRope Implant System, the procedure is designed to accelerate recovery for high ankle sprains, particularly in athletes, and can decrease the chances of long-term damage that can occur with high ankle sprains.
Tagavailoa had the procedure on his left ankle in 2018 after being injured in the SEC Championship Game against Georgia. He returned 28 days later to play in the College Football Playoff semifinal game against Oklahoma, passing for 318 yards and four touchdowns in a 45-34 Alabama win.
In 2019, he injured his right ankle in a game against Tennessee, underwent the procedure and came back three weeks later to play against LSU, a game in which he passed for 418 yards and four touchdowns in a 46-41 loss.
Last season, Tillman became Tennessee's first 1,000-yard receiver since Justin Hunter in 2012. He elected to return for a fifth season after considering a jump to the NFL.
Even without Tillman, Tennessee quarterback Hendon Hooker passed for 349 yards and two touchdowns in the win over Florida.