Smith, who became the first true freshman in more than 30 years to start the season opener at left tackle for the Volunteers, missed all of spring practice due to blood clots in his lungs.
"I've never been in this situation before, so I'm just ready to get back out there and really play football again, to hit somebody again," Smith told ESPN.
According to the report, Smith will need to be monitored regularly and still has a risk of developing more blood clots.
"He's been cleared to do conditioning and drills as long as it's non-contact, and probably about mid-August and sometime before the first game, he will be off the anticoagulants and able to resume contact," Volunteers team physician Dr. Chris Klenck told ESPN. "There's always a risk of a new blood clot forming. There is no scenario where the risk is zero percent. There's still a chance. You just have to be vigilant of signs and symptoms of blood clots."
Klenck said Smith would still face the risks of clots even if he gave up the sport, adding that, "Ultimately it was Trey's decision."
Smith, 6-foot-6 and 320 pounds, started all 12 games last year as a freshman and is considered the team's best lineman. He still must undergo a CT scan before he's cleared to resume contact.
"When he comes back, it may take him a while to play his way back into football mode," said head coach Jeremy Pruitt. "So I'm not sure it would be fair to judge what kind of year he's having until Week 4 or 5 as opposed to the first week. But he loves ball, and I'm just glad he's getting another opportunity."