Police had no further details about the incident.
Bar owner John Devereux said the man had fallen down the flight of stairs at the entrance to the bar, and he understood it had happened after the bar's one-way door policy began at 3am.
Mr Devereux said his thoughts went out to all those affected by what had happened.
It was "absolutely" a shock and upsetting for the staff working at the time.
"It's very, very tragic and sad for everyone involved."
Emergency services rushed to the scene but the man died.
Police were at the premises this morning examining the scene, and the entrance to the bar was cordoned off.
Police are investigating the circumstances of the death.
No further information has been released.