The Zenit St Petersburg manager met with the Italian FA sub-commissioner Alessandro Costacurta and team manager Gabriele Oriali for over two hours in Rome on Monday evening.
It was reported over the weekend that Carlo Ancelotti had turned down the job, and both Gazzetta dello Sport and Corriere dello Sport said on Tuesday that Mancini had agreed to take over and help revive the fortunes of the national side.
Gazzetta said the federation had offered the former Manchester City manager a two-year contract until 2020 worth four million euros ($4.8million) a year.
“Coaching the national team would be prestigious and a source of pride for me because Italy are one of the most important teams in the world,” Mancini told Italian radio on Monday.
Mancini is expected to take over the national team after the final round of Russian domestic fixtures on May 13 and before the May 20 deadline set by the Italian FA.
Zenit however are not happy that Mancini is leaving having only taken over last June, but the club are only fifth in the Russian Super League standings with two matches remaining.
The 53-year-old former Italian international is confident however he can reach a deal with the Russians.
During his 17-year coaching career 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.
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.
Italy have been without a permanent coach since Gian Piero Ventura was sacked after they failed to qualify for the World Cup for the first time in 60 years after losing to Sweden in a two-legged playoff in November.
Italy’s under-21 coach Luigi Di Biagio has been filling the position on an interim basis.
Among the other names being touted are Chelsea manager Antonio Conte and former Leicester coach Claudio Ranieri, now in charge of French club Nantes.