The Uefa president unveiled the plans at a press conference on Saturday that could see the tournament move dramatically away from the usual one or two host country format
Platini presented the idea at a press conference on Saturday and claimed that the proposal had the support of the majority of Uefa's executive committee.
"The Euros in 2020 could be held all over Europe," Platini said. "It could be either one country and 12 stadiums or one stadium in 12 or 13 cities.
"This matter will be discussed very seriously."
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Difficulties have emerged, however, after Turkey launched a bid to host the Olympic Games in the same year, reportedly leading Platini to consider an alternative arrangement.
The hosts were due to be announced in late 2013 or early 2014 but Platini has revealed that a decision on his new plan will be made in January or February of next year.
The proposal is likely to generate controversy as it would theoretically vastly increase the distances between stadiums and therefore the costs of attending the tournament for fans, but Platini pointed out that low-cost airlines could be used.
If Wales, Scotland and the Republic of Ireland were to land the tournament, it would be the first time three countries have joint-hosted a European Championship but Platini's plan would dramatically change the format of the competition.
There will already be a new look to Euro 2016, with 24 teams set to compete in France for the first time. Initially a four team tournament in 1960, Europe's international football showpiece currently features 16 teams.