Aer Lingus has accepted a €1.36bn bid from the International Airlines Group, which owns British Airways.
The Irish carrier, which is part owned by the government and low-cost airline Ryanair, confirmed in a statement that it had accepted IAG's renewed offer of €2.55 per share, following its two previously failed bids.
However, it added that the result will depend on the recommendation of Aer Lingus's board, as well as the Irish government, which owns 25% of the airline, and Ryanair, which has a 29.8% stake.
If the deal goes ahead, the Irish government is set to make around €308m.
BA is the largest operator at Heathrow, while Aer Lingus comes in fourth. IAG is looking to snap up Aer Lingus and the airline's 23 pairs of take-off and landing slots at Heathrow airport.
On 26 January, state-owned broadcaster RTE News reported that Transport Minister Paschal Donohoe was briefing cabinet ministers on the deal and that Minister for Foreign Affairs Charlie Flanagan said that "the Government had some concerns".
Donohoe told RTE News that "the government would give careful consideration to any takeover of Aer Lingus" and that he would "reserve his evaluation until he heard from consultants following a decision on whether to accept the bid by the board".
IAG said in a statement: "IAG recognises the importance of direct air services and air route connectivity for investment and tourism in Ireland and intends to engage with the Irish Government in order to secure its support for the transaction."