Until now the budget airline has had a no-pet policy, meaning its passengers must either put their pets in kennels or forsake their holiday.
But the airline recently suggested it has thought about permitting small dogs in the cabin on short-haul flights to Europe.
“We are open to lots of suggestions,” said chief commercial officer David O’Brien. “It’s one we’re looking at.
“It could be quite difficult. What makes one person happy would make another unhappy.
“But we’d be interested to hear what people think.”
Among the leading budget airlines, Flybe, Monarch and Thomson permit some pet travel, but have restrictions on weight and only allow the pets in the hold.
Easyjet does not allow pets anywhere on the plane.
Only Germanwings allows pets in the cabin, but does not offer the service to or from the UK or Ireland.
Mr O’Brien said the move comes as Ryanair aims to improve its image from “cheap and sometimes cheerful” to “cheap and always cheerful”.
Cats, dogs and ferrets can be taken abroad within the EU without the need for quarantine, but there are strict rules.
They must have been vaccinated against rabies and be treated against tapeworm, be microchipped and have a pet passport or third-country official vet certificate.