ABC News reported on Monday that Khaled and Mahmoud Khayat and Khaled and Abdul Merhi were being held after being taken into custody,
The names have been widely reported, however police have not confirmed them to SBS World News.
Special terrorism powers allow police to hold suspects without charge for up to 12 hours, with authorities to review the detention every 12 hours.
The government has so far declined to reveal any further details of the plane threat, as speculation mounts the alleged plotters intended to use an improvised bomb inside a kitchen grinder or release poisonous gas.
All it will say is that the four - believed to be two fathers and their sons - planned to use a "non-traditional" device and had "an Islamist, extremist terrorist motivation."
The AFP has also refused to say if the alleged plot was targeted at a domestic or an international flight. It’s also unknown when the alleged plot was planned to occur.
Security increased after 'very concerning' terror plot allegations
Airports across Australia have beefed up security procedures after the raids, with travellers being asked to pack light and arrive early for their flights.
Queensland Premier Annastacia Palaszczuk said the revelations about an alleged plot to blow up a domestic flight were "very concerning".
She said the state’s police commissioner Ian Stewart would be discussing the issue with her cabinet on Monday.
Following typical long lines at Sydney and Melbourne airports during the Monday morning peak hour rush, some commuters were surprised to have passed through security quickly and not encountered any extra scrutiny.
Permanent security upgrades could be imposed at Australian airports to protect travellers.
"It may be that we need to look at the security settings at our airports - in particular our domestic airports - for an ongoing, enduring period," Border Protection Minister Peter Dutton warned on Monday.
Australian Federal Police Commissioner Andrew Colvin also flagged, possible long-term changes saying security measures were "always" under review.
But he also said travellers could have confidence in the current security level.
Passenger, hand and checked luggage screening has been ramped up at all Australian airports after the arrests.
The measures have caused long delays at major airports over the past two days, as a 'new normal' takes effect.
Domestic passengers have been told to arrive two hours before flight departures, and international passengers three hours before, to allow for tougher checks including more intensive screening for explosives.
Prime Minister Malcolm Turnbull said the measures would remain in place "for as long as the threat is assessed as requiring them".
Mr Turnbull has also praised Australian police officers for successfully disrupting what appears to be a 'major terrorist plot'.
But Mr Dutton suggested more permanent changes may lie ahead.
"We will take it one day at a time in terms of needing to respond to the threat we know about. But there may be lessons that may be learned here and we can apply those respectively," he said.
Mr Dutton has apologised to travellers experiencing delays and urged all Australians to act as "eyes and ears" for security agencies.
"It may be that bit of information that helps the police to thwart the next plot," he told ABC television.
Some security experts have called for all domestic travellers to made to produce photo identification when checking in.
What we know so far
What was the alleged plot?
The group allegedly planned to use an improvised device to bring down an aeroplane in as Islamist-inspired conspiracy, however police say they have limited information so far about the date, location or specific strategy involved.
What happened during the raids?
NSW and Federal Police swooped on five properties in the Sydney suburbs of Surry Hills, Lakemba, Wiley Park and Punchbowl on Saturday afternoon and found a "considerable" amount of material. But police won't say if they discovered an actual explosive device.
Who is in custody?
Four men were arrested and are assisting with police inquiries. No details have been released by police about their age, background or relationships to one another.
Could it have happened?
AFP Commissioner Andrew Colvin said they treated the plot as credible and there was an intention and "quite possibly a capability" to carry it out. However, he also said there was no reason to believe security at Australian airports has been jeopardised.
What's changing at airports?
Travellers have been told to arrive two hours earlier to make allowances for increased scrutiny. They may notice "intensified" security procedures, but some bolstered arrangements will happen behind the scenes. Travellers have also been asked to limit baggage to make things easier.