British Airways parent IAG has confirmed that it has made a bid for Aer Lingus, but that its offer was rejected.
It issued a statement to the Stock Exchange after reports of the bid prompted a 14% rise in Aer Lingus shares.
"There can be no certainty that any further proposal or offer will be forthcoming," said IAG.
"A further statement will be made if and when appropriate."
A sale of Aer Lingus would require an agreement from the Irish Government, which holds a 25% stake, and Ryanair, which owns 29.9%.
The news of an offer also pushed up shares in Ryanair by 2.3% and IAG by 3.3%.
IAG, which also owns Iberia and Vueling, is believed to be after key take-off and landing slots at Heathrow that are controlled by Aer Lingus.
Ryanair has failed three times to take over Aer Lingus but its bids were blocked by the European Union.
In an attempt in 2012, Ryanair signed a non-binding memorandum of understanding with IAG to allow BA take some of the Heathrow slots.
IAG chief executive Willie Walsh, who was previously chief executive of Aer Lingus, has previously ruled out any interest in acquiring the airline.
