The Belgium international was dismissed by referee Chris Foy after he lost patience during the closing stages of Wednesday night's Capital One Cup semi-final, second leg match at the Liberty Stadium as ball boy Charlie Morgan refused to hand over the ball after it had gone out for a goal-kick.
Morgan fell to the ground as Hazard attempted to get the ball from him, with the Blues forward then trying to kick it from under him but appearing to instead make contact with the youngster.
Hazard escaped criminal action over his conduct after Morgan and his father, Swansea director and hotel owner Martin, decided not to press charges.
But Press Association Sport has been told the FA is looking into the incident.
Hazard already faces an automatic three-match ban but a suspension can be increased in "exceptional circumstances".
There have been strong opinions voiced over the incident.
Former Chelsea winger Pat Nevin claimed he would have done the same as Hazard and branded Morgan's behaviour as "disgraceful".
Nevin told BBC Radio Five Live: "I would have kicked the ball out from underneath the ball boy if he had been lying like that, 100 per cent.
"I was very, very disappointed by the way the ball boy acted, and I say 'acted'.
"He must have been watching footballers, the way he rolled around and pretended to be more injured.
"He only has one job and his job is to go and give the ball back, and what did he do? He keeps the ball. I have to say I was absolutely amazed this morning [Thursday] to find he is 17, not 12, not 13.
"He should know what his action should be in that situation. His behaviour was disgraceful."
Marseille midfielder Joey Barton, on loan from QPR, also sided with Hazard, who is facing internal disciplinary action from Chelsea.
He tweeted: "Hazard only crime is he hasn't kicked him hard enough..."
Barton later posted a further tweet to clarify he was not condoning the kicking of ball boys.
Swansea vice-chairman Leigh Dineen, meanwhile, placed the blame squarely at the door of the Chelsea man and defended Morgan, who has become something of a Twitter celebrity, with his account now having upwards of 80,000 followers.
"The boy went to pick up the ball and he fell over. He didn't hold on to the ball for a minute; it happened over about 20 seconds," he said.
"Had it been 2-0 to Chelsea, I don't think Hazard would have been anywhere near the ball. But I don't think Hazard deliberately went to kick him.
"You can't kick out at anybody. I don't think you can do that. If it was done on the field of play, there would be plenty of questions to be answered."
Steven Martens, the chief executive of the Belgian FA (KBVB) told Press Association Sport: "It's unfortunate and of course it's not something we are proud of. No football authority or person interested in football likes to see acts of violence or lack of respect and this is what happened.
"It might have happened in the heat of the fire but professionals are expected to be able to control themselves.
"They have to be able to control their emotions and when they don't that's unpleasant in general.
"Of course as we are the Belgium FA we don't like it to be a Belgium national squad player but I am very much convinced that Eden himself will realise that.
"Eden is more than intelligent enough to understand that this is going to be a lesson learned for him.
"All of us make mistakes in life."
Professional Footballers' Association chief executive Gordon Taylor does not believe Hazard should face an FA charge over the unsavoury episode.
He told Press Association Sport: "There is obviously a process which the FA have to go through and it is up to them what they decide.
"But I don't think the young lad involved would want to see Hazard punished further.
"The referee made the correct decision on the night and you do not want people to be hung, drawn and quartered for things that happen in the heat of the moment."