The Irish Independent reports the IAA are looking into the incident, which occurred on a plane bound for Germany last Friday.
The two passengers, who were off-duty Ryanair crew members, were permitted to access the cockpit during the Berlin-bound flight.
In a statement to Independent.ie last night, the Irish Aviation Authority (IAA) said:
"In general, access to the cockpit is restricted to operational staff, including staff passengers, unless they are known to the commander and are invited to have access to the cockpit.
"The IAA is currently investigating the incident in question."
A Ryanair spokesperson told Independent.ie that the airline has already carried out an investigation into the incident.
The details of the incident emerged when a passenger on the plane named Bridget approached the publication to say how shocked her and her husband were to see the passengers exit the cockpit and return to their seats at the back of the plane.
The passengers, it is reported, were seen drinking alcohol in Dublin Airport earlier. They claim the pair returned to the cockpit again for landing.
Ryanair later confirmed that after an investigation it found three off duty employees had been travelling on the flight to Berlin.
Bridget and her husband departed Dublin at 2.30pm on a Ryanair flight to Schoenefeld airport, Berlin, on Friday.
“The plane had taken off and we saw them coming out of the cockpit when we were in the air,” Bridget told independent.ie.
“They couldn’t have been in the toilets. The air hostesses check the toilets when you’re ascending and they have to make sure everything is locked.
“My husband noticed them and said ‘those girls are coming out of the cockpit’.
“Later, when the captain said ‘we’re getting ready to descend’, the two girls went back up. They were laughing and giggling and taking photos of each other,” she added.
The passenger told the Independent the two women were wearing tags around their necks but they were not in uniform.
“With things being so strict since the Alps crash, I don’t think this should be allowed," she continued.
“The two of them had a tag around their neck that you’d wear if you were staff or something. But at the same time I don’t think they should have been there.
“Years ago, you could get the kids up to see the captain in the cockpit but now, no one should be allowed up there during a flight.”
Robin Kiely, head of communications at Ryanair, said the company has investigated the matter.
"These were three Ryanair employees travelling off duty," the airline said.
"All three were wearing their Ryanair ID and were known to the flight crew. Following the investigation the matter is now closed."
The airline refused to comment on its policy for passengers, including off-duty staff, being in the cockpit.