Conte, who led Juventus to the Serie A title last season, is accused of failing to report match-fixing in two games in the 2010-11 season when he was coach of Siena, then in Serie B.
On Wednesday, the Italian football federation (FIGC) tribunal said a proposed three-month ban agreed between Conte's lawyers and the federation prosecutor Stefano Palazzi was insufficient.
It called for them to come up with a tougher penalty proposal or to go to a full sporting trial.
Frantic negotiations failed on Thursday and Juventus President Andrea Agnelli blasted the federation, accusing it of incompetence and launching an unjustified "new attack" on the club.
The federation has said it aims to reach a verdict by August 10.
Juventus were stripped of the Serie A titles they won in the 2004/2005 and 2005/2006 seasons following the so-called Calciopoli match-fixing scandal.
The matches involved in the charges were between Novara and Siena in May 2011, which ended 2-2, and between Albinoleffe and Siena in the same month which ended in a 1-0 defeat for Siena.
On Wednesday, Siena had six points deducted for the forthcoming Serie A season after their plea bargain was accepted at the second attempt.
In total, 13 clubs and 45 players and training staff are facing disciplinary charges over the latest match-fixing allegations.
The "Calcioscommesse" scandal echoes earlier match-fixing cases which tarnished Italian soccer in the 1980s and before the 2006 World Cup.
Prosecutors believe an international gambling ring paid players to throw matches. Dozens of current and former players in teams ranging from the Serie A top division down to the lower leagues may have been involved, according to investigators.