It is understood McGregor lashed out after the man turned down a free drink from the star, who had offered his own brand of whisky to everyone inside the venue.
Footage shows McGregor entering the pub and walking up to the bar before the incident took place.
McGregor has spoken to detectives about the incident but was not formally arrested over the matter.
A file has been passed by police to Ireland's Director of Public Prosecutions to make a decision over whether to charge the McGregor.
A Garda spokesman said: "(We) are investigating an incident at a pub in Drimnagh, Dublin, on April 6.
"No arrests have been made. Investigations are ongoing."
Last year, McGregor was convicted of disorderly conduct after attempting to confront UFC rival Khabib Nurmagomedov on a bus full of fighters in New York.
McGregor ran alongside the bus, grabbed a metal trolley and threw it, shattering the bus's window.
He was sentenced to five days of community service and to attend anger management classes after appearing in court in New York.
In March, CCTV footage emerged of McGregor stamping on the mobile phone of a fan in Miami.
The former UFC featherweight and lightweight champion was arrested and charged with strong-arm robbery and criminal mischief over the incident involving 22-year-old Ahmed Abdirzak's phone.