At a meeting with Assembly Sports Minister Alun Pugh on Tuesday it was decided to explore a potential joint bid with Scotland.
"It's worth investigating if Scotland and Wales could put a bid together," FAW secretary David Collins said.
Collins is also keen to bring the Uefa Cup final to Cardiff in 2011 or 2012.
A bid to host the 2008 European Championship finals was abandoned in 2002 when Scotland instead chose to partner the Republic of Ireland, only to be unsuccessful.
Wales were hampered by having just one stadium that met European football's governing body Uefa's 20,000-capacity guidelines - the 75,000-seater Millennium Stadium.
But with Swansea City FC's 20,000-capacity Liberty Stadium now finished and Cardiff City FC's new 30,000-seater home at Leckwith set to get the green light, the FAW is now in a stronger position