But Kelly cautioned that Brooks' recovery will be a "slow process."
According to a statement released by Brooks' family last week, the surgery to remove the "large brain tumor" was successful, and the family is awaiting results of a biopsy.
"We are grateful for the work and care of the medical staff helping Greg through these challenges and for the concern and love poured out by so many in the Louisiana, Arkansas and national sports communities," the family said. "This means the world to us at this difficult time.
"Greg continues to fight, and we await further clarity on the extent of that battle."
Kelly said Wednesday that Brooks, a former Arkansas transfer, had been experiencing what was believed to be vertigo earlier in the year but that it turned out to be a symptom of the tumor.
Doctors discovered the brain mass after ordering an MRI two weeks ago when Brooks complained of dizziness.
Kelly has said that Brooks told him he was insistent about playing again this year. Kelly said he saw Brooks on Monday during a "heavy rehab" day and that Brooks was able to make eye contact and recognize him.
"He was up on his feet and moving around," Kelly said. "But still, there's a long journey for him."
Arkansas coach Sam Pittman, who was in town for the Razorbacks' game against LSU on Saturday, said he was able to go to the hospital and visit Brooks.
"We love him," Pittman said. "It was something I wanted to do and wanted to show the family the respect they deserve."