Italy are looking for a new coach after Gennaro Gattuso stepped down following the Azzurri's failure to qualify for a third consecutive men's World Cup.
Bonucci, who worked as an assistant to Gattuso and is a technical coach in the national team set-up, said: "If we want a radical change in the national team, I'd say the right man for the job is Pep Guardiola. It's very difficult, but dreaming costs nothing."
Guardiola, 55, whose contract with Manchester City expires in June 2027, has often expressed his desire to coach a national team at a major tournament before he retires.
He has already had a glittering coaching career, with spells in charge of Barcelona, Bayern Munich and City having seen him win 40 major trophies, including three Champions League titles.
Leonardo Bonucci is keen for Pep Guardiola to join him in the Italy set-up. Image Photo Agency/Getty Images
Napoli coach Antonio Conte and Juventus manager Massimiliano Allegri are the current frontrunners for the vacant role.
The failure to qualify for four-time World Cup winners Italy resulted in the country's football federation president Gabriele Gravina resigning amid political pressure.
Gianluigi Buffon, the 2006 World Cup winning goalkeeper, also stepped down as the team's delegation chief.
A new president of the FIGC will be elected on June 22.
Italy are in need of a major shake-up, according to Bonucci, who was a key player in Italy's European Championship triumph in 2021.
"We need to have the courage to face up to what's happening so that we can regain the respect of the whole world and become that great national team that was world champion," he said.
"The important thing is to rebuild Italian football, starting from the ground up, starting with the defence.
"Italy needs time and a partnership between politics and football so that both can move in the same direction. There are young players with a lot of talent; we need to nurture them and let them develop, and start afresh. The only magic formula is time."
