Platini said UEFA were waiting from feedback from the 53 European member associations before making a decision - in the past the European Championships have been in just one or two countries.
The Football Association have already registered their interest in hosting the Euro 2020 final at Wembley Stadium should the new format be brought in.
Platini told a news conference in St Petersburg: "It is an idea that will be discussed by all national associations within their relevant meetings.
"It is an idea and that concerns the 60th anniversary of the Euros in 2020, and to carry the game further than just played in one country but extend it to 12 European cities.
"Sometimes it is a bit costly and some countries cannot host the Euros because of the forbidding cost. We are waiting for feedback to say whether they like it or not and whether in 2020 we can organise a Euro in several European cities - but only 2020 mind you.
Meanwhile, Gibraltar has been admitted as a provisional member of UEFA after a long battle by the tiny British colony.
The Gibraltar FA is one of the oldest in the world but its inclusion in UEFA was blocked by Spain until a victory in August in the Court of Arbitration for Sport (CAS).
UEFA said a decision on the admission of the Gibraltar as a full member would be taken at the Congress in London in May.