UEFA supremo Michel Platini announced the decision yesterday to depart from the standard format of staging the finals in one country or a co-hosting arrangement.
And FAI officials believe that the successful staging of the Europa League final two years ago in the Aviva will be a huge advantage when they make a case to UEFA for Dublin to be a host city.
"We welcome the news. We are interested in being a host venue and this development takes that prospect into concrete territory," an FAI spokesman said.
UEFA general secretary Gianni Infantino announced at a press conference: "UEFA Euro 2020 will be staged across the continent, in various major cities, following a decision taken today."
A 'Euro for Europe' follows an initial idea by UEFA president Platini. But there are logistical issues involving tax laws and fan transport, and UEFA will consider having regional 'hubs' such as Scandinavia for group games.
Jonathan Ford, chief executive of the Football Association of Wales, confirmed it would make a bid with the Millennium Stadium - perhaps as part of a British/Irish hub.
"This rules us very much in. We now have to see how can this work on a logistical basis," said Ford.
"If we are part of a hub including Glasgow, Dublin and an English city this could be very exciting."