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 World Cup, Italy's first-round exit prompted Cesare Prandelli to depart as national team boss, and he has since taken up the role vacated by Mancini in Istanbul.
That move has paved the way for Mancini to take over as Italy head coach, and the former Manchester City and Inter boss would be humbled to be offered the job.
"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."
Mancini worked with Balotelli during spells as Inter and Manchester City boss, but on both occasions the pair became embroiled in heated disputes over the striker's disciplinary issues.