FIGC is yet to replace Gian Piero Ventura, who presided over Italy's shock 1-0 aggregate defeat to Sweden in the World Cup qualifying play-off as the Azzurri failed to reach the showpiece tournament for the first time since 1958.
Conte was at the helm between 2014-16, guiding Italy to the Euro 2016 quarter-finals before joining Chelsea, where he won the Premier League title last season and the 48-year-old – who is reportedly unhappy at Stamford Bridge over transfers – wants to work with the national team again, according to Fabbricini.
"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," Fabbricini – who was named commissioner on Thursday after an election failed to find a replacement for former president Carlo Tavecchio – told reporters.
"There's no-one in pole position, we have to evaluate the pros and cons.
"We also have to evaluate the availability of the Federation, and explain to those who will come after us that there will be new governance.
"Now though we'll evaluate what to do, along with [sub-commissioner Alessandro] Costacurta."
Chelsea's title defence is almost over after Wednesday's surprise 3-0 loss at home to Bournemouth left the Londoners 18 points behind runaway Premier League leaders Manchester City.