According to a story in Sunday's The Independent newspaper, European football's governing body wants to have an event that would include Brazil, Argentina, Mexico and Japan.
There is precedent for continental championships inviting outsiders, with the United States, Mexico and Costa Rica having regularly competed in the Copa America for the past two decades.
FIFA are certain to regard a revised format of the European Championship that brings in big-name teams from outside as a threat to the World Cup, which is their biggest source of income.
"As is known, UEFA and its member associations are looking at reforming national team competitions, and this process is ongoing," a UEFA spokesman told Press Association Sport.
"We would not be in a position to comment on any specific ideas that are being considered."
The Independent writes that a senior advisor to UEFA president Michel Platini has said: "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?"
To invite outsiders would lead to more commercial opportunities in other continents for UEFA.
Borrowing on the idea of the Copa America would be another major change for UEFA with respect to the European Championship.
The European football body has already decided to expand the tournament field at Euro 2016 from 16 to 24 teams.
Another big alteration to the European Championship will be seen in 2020, with games expected to be played in 13 cities.
That UEFA may be considering plans for a tournament to rival the World Cup should come as no surprise.
FIFA president Sepp Blatter and Platini are understood to have strained relations, and the former has come under fire from Premier League clubs in England over the possible switch of the schedule of the 2022 World Cup in Qatar from the summer to the winter.
At last week's FIFA executive committee meeting in Zurich, the Premier League clubs voiced strong opposition to a winter schedule. FIFA have set up a task force in the hope of finding a way forward.
Another incentive for UEFA to have a European Championship with teams outside the continent taking part is, according to the senior advisor to Platini, to combat FIFA's plans to reduce Europe's influence within the international governing body.
"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)," the advisor said.
If the plans for a revolutionary new European Championship that includes Brazil, Argentina, Mexico and Japan do go forward for UEFA, there will be critics who claim the event is not as universally inclusive as the World Cup.
Some detractors to the World Cup, however, say the tournament is not as competitive from top to bottom because weaker nations are involved.