The 58-year-old, sacked by Bayern Munich in September, held talks with Italian federation (FIGC) officials in Rome last Monday, according to reports published in several newspapers including Corriere dello Sport and Gazzetta dello Sport.
One of the reasons given was that Ancelotti believes he can get a job with a leading European club. The FIGC could not immediately be reached for comment.
Italy, currently at an all-time low of 20th in the FIFA rankings, have been without a permanent coach since November when Gian Piero Ventura was sacked following their failure to qualify for this year's World Cup in Russia.
Luigi Di Biagio took charge of the team for their friendlies against Argentina and England in March on an interim basis.
Ancelotti, a former midfielder, is one of Europe's most successful coaches, having won the Champions League with AC Milan and Real Madrid, plus domestic league titles with Chelsea, AC Milan, Paris St Germain and Bayern Munich.
Mancini is currently coach of Russian side Zenit St Petersburg.
Former Chelsea, Roma, Juventus, Inter Milan and Leicester City coach Claudio Ranieri, now at Ligue 1 club Nantes, was also reported to be in the running but was considered an outsider.
(Writing by Brian Homewood in Bern; Editing by Toby Davis)
