The Football Association is looking into the incident where Arsenal boss Unai Emery kicked a water bottle into the crowd at Brighton.
The Gunners manager immediately apologised but the FA is considering whether to punish him.
The Spaniard went to speak to the home supporter after the incident and at full-time after the Gunners drew 1-1 at the Amex Stadium on Boxing Day.
"I said to them I'm sorry. It wasn't hard but it touched one supporter," Emery told the BBC afterwards.
Former Manchester United boss Jose Mourinho received a touchline ban for kicking a bottle of water against West Ham in 2016.
He was also sent to the stands during his side's 1-1 draw after lashing out at the bottle in frustration, following referee Jonathan Moss' decision to book Paul Pogba for diving.
He admitted improper conduct and picked up a one-match suspension.
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