The report says Arsenal believe a precedent was set when Chelsea midfielder Nemanja Matic appealed his sending off for violent conduct after reacting angrily to a bad tackle from Burnley's Ashley Barnes.
Matic saw his suspension cut from three to two games.
Cesc Fabregas also had a three-match ban reduced last season. On that occasion the FA cut it to one game after he kicked a ball which hit West Brom's Chris Brunt in the face.
After Saturday's match, Arsene Wenger criticised his player for reacting.
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Diego Costa clashes with Gabriel
He said: "Of course. We warn them not to get involved - and I don't understand Gabriel because he usually looks a calm boy.
"For me, it shouldn't be difficult to stay calm. It's not. I don't believe so.
"You have to be above that. That's part of the game. To be professional, to me, is to deal with that."
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