Aer Lingus has rejected a higher offer from British Airways parent IAG.
IAG confirmed a revised bid was made on December 29 but was rejected by the Aer Lingus Board.
The proposal consisted of a cash offer of €2.40 per Aer Lingus share, subject to certain pre-conditions.
The original offer for €2.30 per Aer Lingus share was also dismissed as too low.
"There can be no certainty that any further proposal or offer will be forthcoming," said IAG.
A takeover would give IAG crucial take-off and landing slots at Heathrow but it would need the approval of Ryanair, which owns 29.9% of the company and has failed several times to take it over.
It would also need the backing from the Irish government, which owns 25% of Aer Lingus.
IAG chief executive Willie Walsh joined BA from Aer Lingus in 2005 and set up IAG six years later when BA merged with Iberia. It has since acquired Vueling.
