The Independent on Sunday reports that sides like Brazil, Argentina, Mexico and Japan could be invited to the tournament as early as 2020.
The tournament increases to 24 teams in 2016 but by inviting non-Europeans, UEFA believe they can make the competition a genuine rival to the World Cup.
The Independent's report says that the plans are still being finalised, let alone approved, but they quote a senior adviser to Platini as saying: "The ideas are at an early stage but they are very feasible. The South Americans have been doing it for decades, inviting teams from outside their continent to take part in the Copa America. So why cannot Europe?”
Since 1993, the Copa America have invited countries from outside of South America into the competition.
Mexico and Japan have both been invited to compete in the next edition in Chile in 2015.
The report says that the idea is "another sign of the growing rift between Platini and FIFA's president, Sepp Blatter."
Platini's adviser says: "Many in FIFA are talking of cutting back Europe’s power, reducing the number of European teams in the World Cup (currently 13 out of 32 in 2014) and also our representation on the FIFA executive (eight out of 24).”
Platini has already got the go ahead for a radical new idea for the 2020 European Championship which will be hosted in 13 cities around the continent as opposed to all being hosted in one or two countries.
32 countries have since declared an interest in hosting matches in that tournament.