A man and a seven-year-old boy were seriously injured in the crash. It's understood the man, who is originally from Poland but living in Dublin, is a regular jumper with the club and he went to the crash site after the crash.
Just the pilot and the young boy were on board when the plane crashed.
Emergency services remain at the scene where the crashed plane is partially submerged in water on bogland near Mount Lucas, a source has said.
The Air Accident Investigation Unit has confirmed it is investigating the circumstances of the crash. Two people died in County Antrim on 19 April while another plane enthusiast died on May 4 in Ballina. "A rescue/recovery operation is under way".
It crashed near the Irish Parachutists Club in County Offaly, Ireland.
It was located a number of kilometres from the airfield in bogland and a rescue and recovery operation is now underway. Witnesses then saw the aircraft crash shortly afterwards. There is no confirmation of any deaths at this point in time.