The tournament switches to 24 finalists in 2016, which will be hosted by France, so only a handful of single candidates could realistically hold the championship.
"UEFA has a history of joint bids .so this is certainly possible," said Infantino following a two-day meeting of the executive committee.
"We have to bear in mind there will be 24 teams which means at least nine stadia."
The first European Championships to be jointly hosted was in 2000 when Belgium and the Netherlands shared the finals followed by Austria and Switzerland in 2008. This year's finals are being jointly hosted by Poland and Ukraine.
"Turkey had and has, unfortunately, some issues. It is now up to the Turkish FA bodies to take the appropriate decisions," said Infantino.
"It is their responsibility. They know what they have to do. We will look into this matter if they don't take any decisions. We have zero tolerance on match-fixing and it is important they take the right decisions."
