Etihad was set up in 2003, with UAE's capital Abu Dhabi as its hub.
It has close ties to Manchester City -- the airline's chairman Sheikh Hamed bin Zayed Al Nahyan is a half-brother of the football club's owner Sheikh Mansour.
In July, Man City confirmed the City of Manchester Stadium at Eastlands would be renamed the Etihad Stadium after striking a 10-year partnership agreement with the airline.
However, it is unclear how far talks between Etihad and the Government have progressed and they might not result in any deal, the report states.
Discussing a possible sale, Mr Varadkar said recently: "What I can say is that the Aer Lingus stake was held for strategic reasons and having studied the matter over the summer, I don't think that really stands any more." If the sale goes ahead, clauses may be introduced that would ensure the retention of Aer Lingus' valuable Heathrow slots for access to Irish airports.
The slots are considered a prime asset of any airline.
The most likely buyer of Aer Lingus remains International Airlines Group, the parent company of British Airways.
James Hogan, Etihad's chief executive, met Taoiseach Enda Kenny at the Global Irish Economic Forum in Dublin. Mr Hogan announced 100 new jobs for cabin crew based in Ireland.
Aer Lingus shares closed at €0.64 at the weekend, valuing the airline at €338.94m and the Government stake at €84.7m.
A Government report in June recommended selling the airline along with a series of other national assets to raise €5bn for the exchequer.
Any sale of the Aer Lingus stake may yet be scuppered by the large deficit in its pension scheme. The shortfall was put at €400m last year.
Other parties interested in buying the stake include Air France and Germany's Lufthansa.
In September, Tanaiste Eamon Gilmore said no decision had been made by the Government on selling its shares.
Speculation that Ryanair, which currently owns a 29.8pc share in Aer Lingus, may tender a bid for the Government's stake have been dismissed.
"Ryanair would welcome another financially strong airline/investor acquiring the government's 25 percent stake, which could then work with Ryanair and other like-minded shareholders to restore shareholder value, which has been destroyed over the past five years by the board and management of Aer Lingus," it said last month.