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.
Next week, all 53 member nations of UEFA will be invited to bid to stage the 2020 tournament and will have until mid-May to declare their interest. Voting will take place in late 2013 or early 2014.
Turkey, who missed out by one vote for the 2016 tournament, may again consider running but their chances will depend on how quickly they sort out the match-fixing problems that have overshadowed their domestic football season.
"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."
An Istanbul court is trying 93 defendants, including the chairman of champions Fenerbahce, Aziz Yildirim, on charges of rigging matches.
