Saban, 69, said that Alabama's doctors will continue to evaluate him but that he doesn't anticipate any issues.
"I'm feeling fine, so you don't need to worry about me," Saban said on Monday.
Saban's positive test came from last Tuesday's round of testing. That would make Friday the earliest he could return from the SEC's mandated 10-day quarantine.
According to SEC protocol, at least 24 hours must have passed since last fever without the use of fever-reducing medications and symptom improvement (cough, shortness of breath, etc.) has occurred, in accordance with current Centers for Disease Control and Prevention guidance for isolation.
Saban missed his first game in 13 seasons as Alabama's coach last Saturday. Offensive coordinator Steve Sarkisian assumed his duties as interim head coach.
The Crimson Tide beat rival Auburn handily, 42-13, but Saban said it was difficult to watch from home.
"I think I did yell at the TV a couple of times today," Saban said after the game on Saturday. "A couple of times when we made some mistakes in coverage. A couple of times when we missed some tackles. A couple times when Mac didn't throw the ball to the guy I thought he should have thrown it to."