The revelation came during a press conference in Rome as the airline unveiled new routes in Italy. A record $1 billion (€883 million) investment in Italy is expected to see 44 new routes, 21 at Rome and Milan airports, and 2,250 jobs created over the course of the year.
And O'Leary had high hopes that Francis could be among the first passengers to make use of the new Ryanair connections, when he comes to the Emerald Isle next year.
The CEO said he had already written to the Vatican to suggest the plan, and was confident the cost-conscious pontiff could be tempted.
“He is a Jesuit and he is very clever when it comes to PR so we look forward to flying the holy father in 2018,” O'Leary explained.
Francis has become known for refusing the traditional trappings of the papacy, having declined to move into the sumptuous papal apartment in the Vatican and opting instead to live in a modest boarding house inside the tiny city state.
And around the time of his selection in 2013 there was widespread surprise when it emerged that he not only carried his own briefcase but also paid his own hotel bills.
Though some claim there is a PR element to these moments, Francis's frugality and fondness for mingling with ordinary people predates him becoming pope.
As bishop of Buenos Aires, local buses were his favoured mode of transport and after becoming pontiff he admitted that the thing he most missed was enjoying the anonymity that would allow him to go into Rome and have a pizza.
So it doesn't seem out of the question that if given the choice, the pope would be open to flying on one of Ryanair's famously no-frills planes, perhaps even in economy class.
However, Vatican spokesman Greg Burke explained that the pope and his entourage tend to fly out of Rome on an Alitalia plane and return on the national carrier of the country visited, if possible.
Burke said Alitalia was an “essential part” of papal trips, suggesting Francis is unlikely to be making use of a Ryanair deal any time soon.
This might not stop Ryanair taking other business from the struggling Alitalia, which is currently battling to slash costs to compete with its budget rivals.
Last month, Alitalia's chairman said “drastic action” was needed in order to turn the company around, amid reports that 1,600 new redundancies were on the horizon.
O'Leary has warned the airline against trying to compete with his business model, saying “the unions won't accept it” and offering to work together as a “cheaper and cleverer solution”.
His proposal would see Ryanair scheduling some flights to feed into Alitalia's long-haul services, but whether this comes to fruition will likely depend on Etihad Airways, which owns 49 percent of Alitalia after rescuing the Italian company from bankruptcy in 2014.