The men, aged 28, 56 and 61, were detained at the airport on Sunday night by officers from the Garda (Irish police) Immigration Bureau.
Irish broadcaster RTÃ‰ said the arrests were connected to an "international illegal immigrant smuggling network".
It reported that the alleged scam has been traced to a travel agency in Rome.
RTÃ‰ said detectives believed illegal immigrants have been taken off flights in Dublin and escorted to waiting vehicles, without going through immigration controls.
Aer Lingus has confirmed that two of its employees are being questioned.
In a statement, a company spokesman said: "Aer Lingus is co-operating fully with an Garda Siochana in their investigation.
"As this is an on-going criminal investigation we have no further comment to make."
The three men are being interviewed by detectives at Ballymun and Coolock Garda stations in County Dublin.
Three men, including two Aer Lingus staff, have been arrested as part of an investigation into assisting illegal immigration through Dublin Airport.