Widely regarded as one of the greatest midfielders in history, Pirlo won the 2006 World Cup with Italy and enjoyed a distinguished club career with Inter Milan, AC Milan and Juventus.
The 47-year-old is currently in charge of Dubai's United FC, who compete in the UAE First Division League.
Pirlo managed Juventus during the 2020-21 season, guiding the Turin club to the Coppa Italia and Italian Super Cup titles.
Reuters has contacted the FIGC for comment.
The reported agreement came hours after former Manchester City and Barcelona manager Pep Guardiola rejected an approach to take charge of Italy, a source familiar with the discussions told Reuters on Friday.
The 55-year-old Spaniard held talks over becoming Italy's head coach, with FIGC president Giovanni Malago suggesting financial flexibility could be shown for a candidate of his stature.
FIGC also sounded out Brazil coach Carlo Ancelotti.
Italy have been searching for a new coach since Gennaro Gattuso stepped down in April after the four-times world champions failed to qualify for a third successive World Cup finals.
Italian football is facing one of its deepest crises in decades, and the appointment of a new national team coach is seen as the first step in a wider effort to rebuild a youth development and talent pathway system that has deteriorated significantly in a country where football remains a national obsession.