The Northern Ireland striker upset some Celtic fans by pretending to play a flute in an apparent mimic of an Orange band member.
Pictures of the incident appeared on the front pages of some newspapers in Scotland though and have prompted debate in Northern Ireland.
IFA chief executive Howard Wells is waiting to speak to Healy before making any judgement.
"I put a call into David to speak to him," he said.
Fulham are also making enquiries over the incident.
A club spokesman said: "The team is in Korea for pre-season. The club is looking into the alleged incident."
Hughes told the Daily Mail: "They were chanting 'Where were you on the 12th?', which is the day of the Orange marching bands in Belfast.
"So he simply pretended to play the flute - there was no attempt to inflame the fans.
"Afterwards, some of the fans who had been giving him stick sent over programmes for him to sign, which he did quite willingly."