He is reportedly still in the first stage of the NBA's concussion protocol and has not progressed to conditioning or other strenuous activity.
Parsons suffered potentially career-ending injuries in a car crash last week, with the other driver arrested on suspicion of driving under the influence of alcohol.
The law firm Morgan & Morgan stated the player "suffered multiple severe and permanent injuries including a traumatic brain injury, disc herniation and a torn labrum," via Chris Haynes of Yahoo Sports.
Parsons was acquired by the Hawks last offseason in a trade from the Memphis Grizzlies. He appeared in just five games before the injury, averaging just 2.8 points and 1.4 rebounds per game.
The 31-year-old has not played in more than 40 games in any of the past three seasons since signing a four-year, $94 million deal with Memphis.
Most of the missed time has been due to knee injuries, but the latest car crash has created more physical issues and an indefinite timeline for his return to the court.