The 43-year-old was suspended for 10 months in August, a punishment later reduced to four months on appeal, for failing to report attempted match-fixing by players during his tenure at Siena in the 2010-11 season.
The FIGC have now invited Conte to discuss two games involving another of his former clubs, Bari, whose league defeats to Treviso and Salernitana in May 2008 and May 2009 respectively have recently fallen under suspicion.
A statement published on the FIGC's official website confirmed Conte's appointment with prosecutors Stefano Palazzi alongside former Bari players Giovanni Marchese and Andrea Masiello was scheduled for today.
Another former Bari player, Vitali Kutuzov, will meet prosecutors on Thursday.
Conte seemed relaxed when addressing reporters as he left the FIGC offices this evening.
"It went well, we all talked for a long time then had a coffee break together," he told the Corriere dello Sport.
"I think I've cleared everything up and I'm not worried about facing any new charge. They did ask me questions about the two matches but it was a very cordial atmosphere."