A video on social media is said to show a stamp on a fan by a player.
It's not clear if McBurnie makes contact with anyone.
McBurnie, who is injured, looked like he was trying to step over him with one bad leg, to which he replied " 100%".
The club declined to comment.
The fans invaded the pitch after the second leg defeat.
McBurnie missed the game with a foot injury.
Police arrested a man after Billy Sharp was allegedly attacked by a fan at the end of the game.
A supporter charged at Sharp as the player stood on the sideline.
After the two legs finished 3-3 on aggregate, Forest won on penalties.
Following the incident involving Sharp, the Professional Footballers Association has called for a review into matchday security and fan disorder.
The EFL condemned the pitch invasion at Forest, and warned it could consider measures if similar occurrences happen in the future.
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