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Mancini, 53, is among the favourites to lead the four-time World Cup winners, with Chelsea manager Antonio Conte and former Bayern Munich coach Carlo Ancelotti also being touted as candidates.
“When you’re abroad you always miss your country,” said Mancini in an episode of “The Lords of Football” series with Sky Sports, which will be broadcast on Saturday.
“When you are in Italy, you sometimes criticise it rightly. You go abroad and you miss this feeling.
“You become nostalgic for the past when we were young, in the ’70s and ’80s when we saw the Italian national team playing with great emotion.
“You never know in life, I think that coaching Italy one day would be an extraordinary thing of enormous prestige.”
“In the meantime, though, I’ll try to win and do my best with Zenit,” he added of his current team, who are struggling down in fifth in Russia.
Giampiero Ventura was fired as coach last November, days after Italy’s shock failure to qualify for the World Cup for the first time in 60 years.
The new boss is expected to be appointed by June, with Italy Under-21 coach Luigi Di Biagio in interim charge for friendlies against Argentina and England next month.
Mancini led Manchester City to their first English title in 44 years in 2012, and won three Serie A titles with Inter Milan and Italian Cups with Inter, Fiorentina and Lazio.
And the former Italian international has said he wants to take over as national coach to fulfil his dream of winning the World Cup.
The former Lazio and Sampdoria forward never became a regular with Italy during his 10-year international career, during which he won 36 caps and scored four goals.
He reached the semi-finals of Euro 1988, and was in the squad that finished third in the 1990 World Cup on home soil.
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