Italy have been on the hunt for a new manager since sacking Gian Piero Ventura back in November following the country's failure to progress through to the 2018 World Cup after a surprise play-off defeat to Sweden.
Former AC Milan boss Ancelotti has been out of work since he was sacked by Bayern earlier this season, and there are rumours he is itching to return to coaching.
Ancelotti, who has managed teams to league title triumphs in Italy, England, France and Germany, will have to lift a nation who failed to qualify for this summer's World Cup.
"Carlo was in Rome for personal reasons", he told Sky Sports. The chosen hotel was the one where I always stay and we met there. We didn't talk about figures.
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"You have to talk about many things, the program and finances, but we could not talk about them".
However, Costacurta played down his meeting with Ancelotti and insists no official offer has been made.
"Since we are loyal to the rules, we talked about something else". It's true there's a vision in which we can see Carlo, like others, on the national team's bench, but the rules are important and we must follow them. "Unfortunately we spoke about something else".
Among the other names touted were Zenit St Petersburg coach Roberto Mancini, Chelsea boss Antonio Conte and former Leicester coach Claudio Ranieri, now in charge of French club Nantes.