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 he could still face a police investigation after the South Wales force revealed they were following up three calls from members of the public.
"South Wales Police has received a number of calls following an incident involving a ballboy at the Capital One Cup semi-final," a spokesman said.
"Three calls have been received from members of the public living in Sussex, Kent and West Wales which are being followed up."
The FA is also looking into the incident.
Hazard already faces an automatic three-match ban but a suspension can be increased in "exceptional circumstances".
Professional Footballers' Association chairman Gordon Taylor has criticised Hazard for his behaviour.
"You can't take the law into your own hands," Taylor told BBC Sport. "He lost his head and had to receive a punishment.
"You can understand the frustration of wanting to get the ball back but his actions were unacceptable and the referee had no alternative."