The Football Association is looking into the incident which saw Arsenal boss Unai Emery kick a water bottle into the crowd at Brighton, The Independent understands.
The Spaniard went to speak to the home supporter immediately after the incident and again at full-time after the Gunners drew 1-1 on Boxing Day.
He apologised but the FA is still investigating the incident.
Emery said: “I said to them apologies because I kicked the bottle after a disappointing action for us in the last minutes. It wasn't hard, but it touched one supporter for them. I said to them I'm sorry.”
Emery had been left frustrated by his side's second-half display when they failed to restore the lead given to them by Pierre-Emerick Aubameyang's fourth-minute goal.
A mistake by Arsenal right-back Stephan Lichtsteiner had allowed Jurgen Locadia to equalise in the 35th minute, with the game finishing 1-1.
