Aer Lingus's shares have climbed from 1.10 euro at the start of January to 1.28, just short of the 1.30 euros that Ryanair offered for the small airline last month.
Ryanair's biggest obstacle is the risk that its proposed 694 million euro ($939 million) takeover could be blocked by European competition authorities and it wants British airline Flybe to take over some Aer Lingus routes to allay their concerns.
But Aer Lingus management said the plan, which would effectively create a new Irish airline, was unrealistic. The European Commission is due to make a decision by March 6.
"It seems to me so far fetched, this proposition, that we don't bother wasting our time on it," Aer Lingus Chief Executive Christoph Mueller told journalists in a conference call.
"We question very much that Flybe will be an independent competitor to Ryanair and we are working from the assumption that we will be around next year when we talk'' at Aer Lingus's 2013 results announcement, he said.
Mueller was speaking after Aer Lingus announced operating profit of 69.1 million euros, up 40 percent from last year. That was slightly above a consensus forecast of 66.1 million euros by seven analysts polled by Reuters.
It said yields per passenger were up 7 percent from last year while passenger numbers were up 1.5 percent at 9.5 million.
The airline will pay a dividend of 4 euro cents per share this year, up from 3 cent last year.