Ryanair has warned that Aer Lingus would likely be broken up if the European Commission blocks the bid by the airline to take over its rival.
The commission is due to rule by January whether Ryanair's third attempt to take over Aer Lingus would restrict competition.
Ryanair's chief executive Michael O'Leary said the airline had received approaches by financial institutions to buy its near 30% stake in Aer Lingus.
It said it may sell it if the EU rejects a package of remedies to address its competition concerns.
Mr O'Leary declined to give details of the approaches.
"If the commission turns down this remedies package, then I think we would then have to seriously consider exiting our investment in Aer Lingus, which will without question result in Aer Lingus being broken up," O'Leary told journalists on the sidelines of the company's AGM in Dublin today.
The remedies package includes commitments by more than one airline to compete on routes where Ryanair and Aer Lingus currently have no competitors.
The commission will talk to the airlines in question before Ryanair submits its final remedies package, O'Leary said. "They have said that they want to take up the packages of the routes and flights and traffic that we have laid on the table. None of them can formally commit until they sit down and discuss it with the European Commission," he said.
The package would see "multiple airlines" starting new routes to Irish airports in Cork, Shannon, Dublin and Knock.
The Ryanair boss declined to name the airlines, but a source familiar with the matter has told Reuters the company was talking to British Airways and Virgin Atlantic about taking over some routes.
See how the Ryanair and Aer Lingus shares are doing here
Aer Lingus has said it expected the commission to reject the bid as the number of routes on which the two airlines compete was higher than when the Commission rejected an earlier bid. The Government has said it is interested in selling its 25% stake in Aer Lingus when market conditions are right.
Shareholders at the company's AGM heard today that Ryanair is confident it will meet its full-year profit guidance. The airline had told investors in July that it expected to post a profit of between €400-440m for the year to March 2013.
