But concussion experts said this week that hopes for a rapid return could be premature. They said Tebow likely would have to be symptom-free for seven consecutive days before he could be cleared to play by a neurologist.
"It would not be unexpected that his symptoms clear up as the week goes along, and he'd be good to go next weekend," said Dr. Robert Cantu, a clinical professor of neurology at Boston University. "But there's no way anybody today can make that statement."
Meyer said repeatedly Monday that Tebow's return would be up to the medical staff.
He said Tuesday that Tebow, who still is battling headaches, is being placed in a "non-stimulus environment," meaning no film study, no TV and no reading. He attended a brief team meeting Tuesday and briefly discussed the game plan for LSU.
Tebow also is going through brief exercises each day to test his coordination and balance.
The training staff also is giving him memory-testing exercises and comparing the results to baseline testing that each player undergoes in the summer.
"This isn't a turf toe or a shoulder. This is a concussion," Meyer said. "He's a grown man, so he's going to take care of himself."
Many of his teammates expect him to be ready for LSU. For that to happen, he would have to resume physical activity by Saturday and then remain symptom-free.
Cantu said Tebow needs to be brought back progressively.
"You don't go back to taking hits the first day you're back," Cantu said.
Tebow also has been suffering from the flu, which could make it hard for doctors to determine if his headaches and nausea are caused by illness or the head injury.
The fact that Tebow felt better Monday is a good start, but the headaches would have to go away by Saturday - and stay away - for him to have a chance to face LSU.
"If he's asymptomatic for four days, and then he starts getting a headache, it starts over," said ESPN football analyst Merrill Hoge, whose NFL career was ended by multiple concussions. "So if this happens next Tuesday, then he shouldn't play at all, no question."
Hoge, 44, knows what he's talking about. With the Chicago Bears in 1994, he returned to practice five days after sustaining a major concussion. He said he couldn't remember new plays installed in the offense and suffered from headaches at night.
Four weeks later, he suffered another concussion that ended his career and threatened his life. Hoge rehabbed for 18 months and had to re-teach himself how to read.
A second concussion can be especially dangerous if it follows too closely after the first. That is why experts emphasize that a concussed player has to be free of symptoms for a week before returning to action.
"Those seven consecutive days are very important, and so many people cheat them," Hoge said. "So Tim Tebow wants to go play LSU and then be brain dead the rest of his life? That ain't worth it."
The severity of Tebow's concussion is not publicly known. Cantu said it usually takes about a week before a concussion can be graded I (least severe), II or III (most severe).
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