Antonio Conte almost quit Chelsea last summer over transfer disagreements with the board.
He eventually signed an improved, but not extended, contract at Stamford Bridge.
But a rocky season in west London, coupled with another transfer window where Chelsea struggled to sign players until the deadline, means Conte is looking for a way out.
And Italy’s new commissioner Roberto Fabbricini says Conte is one of a number of managers eyeing the vacant role.
“The names are the ones you’ve already heard,” he told reporters.
“(Roberto) Mancini was in Rome but we didn’t speak with him.
“Conte seems eager to rejoin the Azzurri, (Carlo) Ancelotti opens and closes the door while (Claudio) Ranieri remains in the mix.
“There isn’t a favourite, but we have to look at the positives and negatives.
“Whoever has made Italian football proud will be taken into consideration.”
Italy failed to qualify for the World Cup under manager Giampiero Ventura, who left the Azzurri following their disastrous campaign.
Ranieri, since being sacked by Leicester, has rebuilt his career yet again – this time at Nice.
Ancelotti is currently out of work after leaving Bayern Munich last summer and is a possible candidate for the Chelsea post if Conte himself moves on.
As for Mancini, he is currently in charge of Zenit, having managed at Galatasaray and Inter Milan since leaving Manchester City in 2013.