UEFA said last week that Italy, France and Turkey were considering single bids with Norway and Sweden looking at co-hosting the championship, which will be the first to have 24 teams.
"We do not have a problem with a joint bid for Euro 2016. If it were France, it would be a friendly and neighbouring country. If it were not technically and politically possible, we would go ahead alone," Giancarlo Abete told Italian radio.
"With great transparency, we want to check if a way forward can be found. If it is not possible, we are not scared of competing by ourselves."
Italy missed out on Euro 2012 to Ukraine and Poland partly because of the decaying state of many Serie A stadiums, which were built or refurbished for the 1990 World Cup.
Huge investment in difficult economic times would be needed to revamp Italy's footballing infrastructure, making the idea of a joint bid more appealing.
France do not want to co-host the tournament with any other nation, French federation chairman Jean-Pierre Escalettes told reporters earlier this month.
"We stick to our previous statements. We go for it on our own and we don't have any plan whatsoever to launch a joint bid with another nation," French Federation spokesman Francois Manardo said on Monday.
There is no love lost between Italy and France on the field and off it.
Italy beat Les Bleus on penalties in the last World Cup final in Berlin three years ago and outspoken France coach Raymond Domenech is constantly pilloried by Italian media.
Bid dossiers have to be presented to UEFA by February 15, 2010 with a final decision made on or around May 27 next year.
