The 45-year-old Conte is regarded as one of the best coaches in Europe after leading Juventus to three successive Serie A titles.
He unexpectedly resigned from his post in Turin last month and is now the front-runner to replace Cesare Prandelli in the Italy hot seat following their disappointing 2014 World Cup showing.
FIGC president Carlo Tavecchio confirmed they had been talking with Conte earlier this week, and discussions remain ongoing, with the organisation hopeful of making an announcement next week.
An FIGC spokesperson told Perform on Thursday: "Negotiations between the FIGC and Antonio Conte as national team coach are still in due course.
"Both parties will be meeting by the end of this week to discuss further details."
Italy failed to make it through the group stages in Brazil, leading to Prandelli's resignation.
Conte is reportedly vying with former Manchester City and Galatasaray manager Roberto Mancini for the position.
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