Varnado became nauseous during a workout Monday and was taken in for tests. He ended up staying overnight when doctors were unable to complete their examination.
Further tests Tuesday failed to show why Varnado became ill.
University spokesman Gregg Ellis says Varnado can return to practice in "a couple of days."
The 6-foot-9 player from Brownsville, Tenn., is one of the top returners after leading the nation in blocked shots the last two seasons. He led the Bulldogs to the Southeastern Conference tournament title and was named MVP.