The Football Association of Ireland (FAI), which previously considered a bid with their Scottish counterparts to host Euro 2008, said preliminary talks had been held between the three associations and that they would explore a joint bid in more detail over the next 18 months.
With the deadline to express an interest expiring later on Tuesday, Georgia said it would go it alone with a bid, ditching an original plan to co-host with Azerbaijan after Baku withdrew its interest in order to focus on a bid for the 2020 Olympics.
Turkey filed its candidacy last month but it is also bidding for the 2020 Olympics, raising concerns over whether Istanbul can host both events in the space of two months.
The competition will be expanded from 16 to 24 teams after this summer's championship, placing a greater demand on bidding countries who will need to have up to 10 stadiums to host matches.
Scotland and Wales, who briefly mulled a bid to host in 2016, would not be able to provide the required number but could do so with Ireland which may be able to use the 82,000 capacity Croke Park Gaelic sports ground, as well as the 50,000-seat Aviva Stadium, built on the grounds of the flattened Lansdowne Road.
Georgia would have to build a number of new stadiums and the country's sports minister detailed its plans on Tuesday after confirming that a formal expression of interest had been sent to UEFA.
Construction of a new stadium in the Black Sea resort of Batumi would start this year, with further new stadiums planned for Gori, Ozurgeti and Zugdidi and major overhauls of stadiums in Tbilisi and the country's second largest city of Kutais, Lado Vardzelashvili told a televised news conference.
Local news agency www.vivil.ge reported that the country's largest stadium, the Boris Paichadze National Stadium, has a capacity of 55,000 with Tbilisi's Mikheil Meskhi Stadium currently holding 25,000.
UEFA requires at least two stadiums of 50,000 seats; three of 40,000 and four of 30,000.
Poland and Ukraine will host this year's competition. Ireland are the only nation bidding to host Euro 2020 that have qualified for the finals that start in just over three weeks time.
