The Juventus coach's legal representatives say their client's statement was unfairly dismissed by the courts
The 43-year-old was initially handed a 10-month ban in August after being charged with failing to report two instances of match-fixing while in charge of Siena.
His sentence was later reduced to four months, but Giulia Bongiorno, Luigi Chiappero and Antonio De Rensis - Conte's lawyers - have now suggested their client's statement, made in a meeting with FIGC prosecutor Stefano Palazzi, was not taken into account.
A statement on the club's official website read: "The sentence passed by TNAS charges Antonio Conte with having been informed by [Cristian] Stellini on March 8, 2012 of the offence committed by the players in the match between Albinoleffe and Siena.
"Therefore, according to the CONI [Italian National Olympic Committee], Conte's failure to report the matter began at least on that date.
"Clearly the members of the arbitration tribunal did not give due consideration to the statement made by Antonio Conte on July 13, 2012.
"[His statement proved] Stellini never informed Conte about any agreements to fix the reverse fixture between Albinoleffe and Siena, he merely reported what had happened in the Siena dressing room after the game.
"A simple observation - after the false accusation regarding Siena v Novara, after falsely affirming that [Salvatore] Mastronunzio had been dropped from the squad for illicit reasons, and no longer able to use [Albinoleffe midfielder Filippo] Carobbio's statements, the TNAS charged Antonio Conte and his defence with an admission of responsibility which in fact never took place.
"This is a mistake which can no longer be rectified. Anyone who has the time and opportunity to read the records will be able to verify as much for themselves."