The 46-year-old, rumoured to be a target for Chelsea to take over from Guus Hiddink at the end of this season, is accused of having failed to denounce an attempt to fix a match while coach of then-second division Siena against Albinoleffe in May 2011.
He has already served a four-month ban handed down by the Italian Football Federation in 2012 after being found guilty of the charge by a sporting court - his sentence was reduced from 10 months on appeal.
Conte, who was Juventus coach at the time of his conviction but was supported by his employers, did not want to head to Euro 2016 with the criminal charge brought by a court in Cremona still hanging over his head.
His lawyers asked for a shortened trial - a decision is due by around mid-May, according to Italian press reports - in order to find out before the Euros whether or not he will face a further sanction.
Conte has always denied any knowledge of the deal between players to fix the match, which his Siena side won 1-0, the same year they were promoted to Serie A and Conte earnt a move to Juve, the club he graced as a player for 13 years.
The calcioscommesse (football-betting) scandal broke in June 2011 and has seen many well-known figures from football serve bans for match-fixing, such as former Italy internationals Giuseppe Signori and Cristiano Doni.
Around 100 people are still awaiting trial accused with various roles in the vast corruption scandal.