Mancini tells RAI state radio, “There has not been contact with the (Italian football) federation but, for a coach, the Italian national team would be a source of honor and prestige.”
Italian media reported over the weekend that Ancelotti informed the federation he was no longer interested.
Under-21 coach Luigi Di Biagio guided Italy on an interim basis in friendlies last month but the team has not had a full-time coach since November when Gian Piero Ventura was fired after the Azzurri failed to qualify for the World Cup for the first time in six decades.
Mancini, a former Italy player, has coached Fiorentina, Lazio, Inter Milan, Manchester City, and Galatasaray to titles.
Nantes coach Claudio Ranieri remains a secondary candidate.
The Italian federation has said it will announce a coach by May 20.
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