Roberto Mancini, Massimiliano Allegri, Luciano Spalletti and Alberto Zaccheroni are candidates for Italy Coach.
Cesare Prandelli resigned after the first round exit from the World Cup, despite only agreeing a two-year contract extension last month.
The race is now on to find a replacement ahead of the Euro 2016 qualifiers in September.
There are several potential candidates, as Antonio Conte and Carlo Ancelotti are unlikely to leave their club positions at Juventus and Real Madrid.
Former Manchester City manager Mancini has worked internationally in England and Turkey with Galatasaray.
He is a free agent after resigning from Galatasaray earlier this month in protest at their transfer strategy.
Another option is Allegri, although he’d be an unpopular pick just six months after Milan fired him for poor results.
Spalletti was sacked by Zenit St Petersburg, but achieved great things with his Roma side in the past and plays attack-minded football.
Zaccheroni is currently the Coach of Japan, but under fire from the media due to a disappointing World Cup campaign.
He was very successful though, as he won the Asia Cup and ensured Japan were the first country to qualify for this tournament in Brazil.