The Football Association of Wales, led by David Collins have met with the Scottish Football Association's Chief Executive Gordon Smith to discuss the bidding process for the event, which is expected to begin late in 2009.
Scotland have already made a bid for the Euros in recent times but failed after their joint bid with the Republic of Ireland was rejected. UEFA specify that all bids must have eight stadiums with capacities of at least 30,000 seats and at the moment Wales have just one stadium that met the criteria, the Millennium Stadium, which can hold in excess of 75,000.
That remains the case, but the FAW are serious about developing Swansea's new Liberty Stadium and using FA Cup finalists Cardiff City's new ground, which is due to open next year.
The Scots already have a number of top eligible grounds, including Hampden Park, Celtic Park, Ibrox, while national rugby stadium Murrayfield also comfortably meets the requirements. However, a joint bid between the pair would still require one more facility to be built.
"The talks at this stage are tentative, but we need to look at the 2009/10 bidding process, with a possible bid for the 2016 event," FAW boss Collins told BBC Sport.
"With the infrastructure being built in Wales we can certainly do it.
"If you look at the size of Austria and Switzerland they're not a million miles away from Scotland and Wales.
"Wales will soon have three venues available so it is possible.
"Euro 2008 has been absolutely superb, I've been based in Switzerland and the whole thing has been exceptional."
Euro 2008 in Austria and Switzerland has been considered a success, while the 2012 event will also be hosted by two countries who made a successful joint bid, Poland and the Ukraine.
Many analysts have suggested that UEFA will expand the competition from 16 to 24 teams after 2012, meaning that Scotland's chances to make a successful solo bid from that year onwards look slim, prompting talks with other organisations.