"We'll definitely consider him and we'll probably call him", Mancini said at his presentation on Tuesday. "He's one of those players who we'd like to see return to what we saw in the European Championships with [Cesare] Prandelli".
During their time at City, Mancini often clashed with the troublesome star. Italy have been without a permanent coach since Gian Piero Ventura was sacked after the four-time world champions failed to qualify for the mega event for the first time since 1958.
But Italy have dropped to their lowest-ever Federation Internationale de Football Association ranking of 20th after the four-time winners missed out on this year's World Cup in Russia.
Mancini says "amid such a hard period, I thought this could be the right time (to take the job)".
"It went the way we wanted, we are happy and Roberto is happy", Fabbricini told journalists.
The new head coach will meet the media for the first time as Italy boss at 12:00 (1000GMT) at the national team's training centre at Coverciano near Florence.
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This will be Roberto Mancini's first worldwide appointment.
Mancini's arrival as Italy boss has sparked rumours that Mario Balotelli will be recalled to the worldwide scene after a fine season with Nice, scoring 26 times in 37 appearances. Age is certainly important because we need to build for the future but there is no set criteria to exclude in this regard.
"I hope to bring the national team back to high levels".
Mancini's first game in charge will be against Saudi Arabia on May 28 - the first of three friendlies in a week, with matches against France and Netherlands also scheduled.
Mancini, a gifted forward in his playing days, won a surprisingly modest 36 caps for Italy and never played at a World Cup, although he was an unused member of the 1990 squad.
His Zenit team finished the Russian Premier League in fifth after beating relegated SKA Khabarovsk 6-0 on Sunday. His first official match will come in the new Nations League in September.
Roberto Mancini will leave Zenit St. Petersburg at the end of the season to become the next manager of the Italian national team.