In a market update this morning, it said: "the board is considering the revised proposal".
The most recent offer, which is the third IAG has made since December, values the Irish airline at €1.34bn (£1bn), or €2.50 per share.
IAG’s previous bids of €2.30 and €2.40 a share have been turned down during the past few weeks. Aer Lingus stated that IAG, which also owns Spanish carrier Iberia, had “fundamentally undervalued” the business in making its initial offer.
The deal would bring Aer Lingus back under the leadership of Willie Walsh, IAG’s chief executive. Walsh was chief executive at Aer Lingus from 2001 until 2005.
The Irish government holds a 21.5 per cent stake in Aer Lingus, and Paschal Donohoe, minister for transport, told the country’s national broadcaster RTE at the weekend that “huge care” will be taken in evaluating any proposal.
Meanwhile, market sources have previously speculated that a deal between the two would be welcomed by rival airline Ryanair. The budget carrier has a 29 per cent stake in Aer Lingus, and is currently appealing a ruling by the Competition Commission that it must reduce this stake to five per cent. Ryanair itself has made three failed attempts to take over Aer Lingus.