However, Ancelotti is now pondering over a reported two-year offer from Azzurri chiefs, and if he accepts the terms, he'll venture into the worldwide arena for the first time in his managerial career.
"It was just an approach", Fabbricini told ANSA after a meeting at a Rome hotel on Monday.
"You have to talk about many things, the program and the finances, but we can not talk about them", he said.
"We agreed that we'd speak again by the end of April, so let's say that we'll know more by that time..." We couldn't talk about the programme and the financial side. It is true, there is a vision that could see Carlo, like others, on the bench of the national team, but the rules are important and we must follow them.
Napoli stun Juventus with late Koulibaly header
Benevento's relegation from Serie A was confirmed on Sunday after just one year in Italy's top flight. Massimiliano Allegri's side face a trickier run-in, as they will face Inter Milan and Roma.
Fabbricini had earlier stressed that the meeting was not an official discussion, even though the Italian federation does consider Ancelotti a candidate. We need people who are available, we can not get close to contracted coaches.
"He was in Rome for family reasons".
Both Ancelotti and Costacurta previously met in London last month to discuss the role in detail.
"We talked about a future scenario though, but we still have a coach under contract".
"But, of course, there are other factors which affect the decision: the desire to work every day, for example".