The former Juventus boss, who left the Bianconeri behind in July, could be announced as Cesare Prandelli's long-term replacement as early as Thursday afternoon.
The Gazzetta dello Sport claims newly-elected Italian Football Federation (FIGC) president Carlo Tavecchio is prepared to offer Conte a two-year deal worth 1.6million euros net each year.
But given the fact the 45-year-old collected a reported 3.5million euro annual salary at Juve, the FIGC is understood to have asked national team kit sponsors Puma to help bridge the sizeable gap.
Conte, a midfielder with Lecce and Juventus, enjoyed three successful years as a manager in Turin, guiding Juve to three consecutive Serie A titles and once into the last 16 of the Champions League.
He served a four-month FIGC suspension from football between August and December 2012 for failing to report his knowledge of attempted match-fixing during his time as the manager of Siena.
The Italy job has been vacant since Prandelli resigned at the end of the World Cup finals in Brazil. The Azzurri failed to progress from a group which also contained England, Uruguay and Costa Rica.