The French club's title challenge could be put into doubt after the sporting director appeared to push the referee during his side's 1-1 draw with Valenciennes
Thiago Silva was sent off two minutes before the break against Daniel Sanchez's side and video footage showed the former AC Milan boss shoving Alexandre Castro in the tunnel.
Should Castro decide to report the incident, the French authorities could slap the capital club with a hefty punishment and the Brazilian with a suspension.
The code of conduct of the Professional Football League (LFP) stipulates that, "in addition to the punishment of the trainer, coach, official or medical staff member, a deduction or suspension of points of the team" can be handed out.
After the game, Leonardo told reporters: "He's a referee who has done 10 matches, this was his 10th, and he has given 48 yellows and five reds.
"This was a calm match and he has brought out seven yellows and one red. I don't understand why we have a referee with nine matches for a big game like this. I don't understand."
PSG saw their lead cut to seven points in the wake of the game thanks to Olympique de Marseille's win over Bastia on Tuesday. They have three games left to play this season.