Mancini left his post at Galatasaray at the end of the season, after guiding the club to a second-place finish in his sole campaign at the helm of the Super Lig outfit.
Despite signing a two-year contract extension ahead of the FIFA World Cup, Italy's first-round exit prompted Cesare Prandelli to depart as national team boss, and has since taken up the role vacated by Mancini in Istanbul.
"Italy would be an honour for me," he told Corriere dello Sport.
"No one called me but I would be proud.
"[The] FIGC [Italian Football Association] need serious and competent men."
He added: "The national team were too old? The age does not matter.
"I love [Mario] Balotelli, but he must grow up. With [Marco] Verratti and [Ciro] Immobile, the team can be reconstructed."
