The former Napoli and Valencia coach is expected to depart after missing World Cup qualification this week.
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Italy were beaten in their playoff final against Bosnia on penalties.
Sky Italia says FIGC will soon announce the move, with Gattuso actually initiating talks over his departure.
Just yesterday, FIGC president Gabriele Gravina had given the 48-year-old his full support publicly.
Sky Italia says Antonio Conte (Napoli) and Massimiliano Allegri (AC Milan) are possible successors, but both are still under long-term contract with their clubs.