Conte left the job for Chelsea after Euro 2016, but replacement Gian Piero Ventura was sacked after Italy lost to Sweden in the World Cup play-off last November.
And speculation over 48-year-old Conte’s future has grown after Chelsea were beaten 3-0 by Bournemouth at Stamford Bridge on Wednesday.
Fabbricini said former Manchester City manager Roberto Mancini, currently in charge of Zenit St Petersburg, Carlo Ancelotti, who is available after being sacked by Bayern Munich, and Nantes coach Claudio Ranieri, who led Leicester City to the Premier League title in 2016, were also candidates.
“The names are the ones you know,” the new FIGC commissioner confirmed after his appointment on Thursday.
“Mancini was in Rome but we didn’t contact him, Conte seems eager to wear Azzurro again, Ancelotti opens and closes the door and Ranieri isn’t out either.”
Ventura was fired after Italy failed to reach the World Cup finals for the first time since 1958 and FIGC president Carlo Tavecchio resigned.
After elections this week failed to return a successor to Tavecchio, the Italian Olympic Commmittee (CONI) appointed Fabbricini as emergency boss for at least six months.
“There’s no-one in pole position, we have to evaluate the pros and cons,” he continued. “Now though we’ll evaluate what to do together with (sub-commissioner Alessandro) Costacurta.”
Former AC Milan great Costacurta was named as one of two deputy commissioners to work alongside Fabbricini.
The 51-year-old former Italy defender played a key role in AC Milan’s ‘Invincibles’ golden generation.
Costacurta spent over 20 years with AC Milan from 1986, winning 23 trophies including seven league titles and five European Cups, before retiring aged 41 in May 2007.
He played 59 times for Italy and finished runner-up at the 1994 World Cup.
After a brief coaching spell he has been working as a television football pundit.
During his career he played under some of Milan’s greatest coaches including Arrigo Sacchi, Ancelotti, Alberto Zaccheroni, and Fabio Capello, winner of four Serie A titles at the San Siro.
“We have to start talks soon,” said Costacurta of their search for an Italy boss.
“The names are those already heard, like Mancini who shared matches with me on the national team and also military service.
“Conte performed a sporting miracle at the last European Championship.”
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