Italian Football Federation president Carlo Tavecchio has suggested Antonio Conte would be his preferred choice as national team boss.
The Federazione Italiana Giuoco Calcio (FIGC) sacked Gian Piero Ventura following Italy's failure to qualify for next summer's World Cup and Tavecchio would like to see Chelsea boss Conte return to his former role.
Conte left for Stamford Bridge after Euro 2016, but, after winning the Premier League title in his first season in west London, has been forced to deny rumours of player unrest this campaign.
Tavecchio was quoted as saying on gazzetta.it: "We are seeking the best. Allegri, Mancini, Ancelotti....these are the names, I say getting warmer. And Conte? Fire."
Juventus boss Massimiliano Allegri, Zenit St Petersburg's former Manchester City manager Roberto Mancini and ex-Bayern Munich chief Carlo Ancelotti appear to be the other main contenders.
Only Ancelotti, though, is not currently in a job.
Italy lost their World Cup play-off 1-0 on aggregate to Sweden to miss out on the competition for the first time since 1958.
Tavecchio laid the blame for their failure firmly at the door of Ventura, saying: "It is all the fault of Ventura, he chose the staff, he has done all of it. We as a federation have never interfered."