O’Leary said there was a “fifty-fifty” chance that he would step down at that time, The Daily Telegraph reported.
“The acid test of a really good company…is can you actually get the next management group to come through. That’s a challenge facing me and the rest of the management team here over the next five years,” he said.
O’Leary has served as chief executive since 1994.
He was speaking at a press conference to mark the carrier’s announcement of new customer service improvements as part of its “Always Getting Better” plan.