Conte, who denies any wrongdoing, is accused by prosecutors in the city of Cremona of "sporting fraud".
The case focuses on 2011, when he was in charge of Siena in Serie B.
The 46-year-old former Juventus boss will become Chelsea head coach after managing Italy at Euro 2016.
Conte has already served a ban imposed by the Italian soccer federation in connection with the 2011 case.
Prosecutor Roberto di Martino has cited a match against Albino Leffe, claiming Conte knew of match-fixing efforts. He requested the sentence and 8,000 euro fine in a closed-doors hearing in Cremona on Tuesday.
Conte's lawyer, Leonardo Cammarata, said the defence is due to make its final statement to the court on 11 April and a verdict is due in mid-May.
A Chelsea spokesman said the club would not comment on an ongoing investigation.
An Italian prosecutor wants incoming Chelsea boss Antonio Conte to get a six-month suspended prison sentence and fine over his alleged role in a match-fixing case, according to his lawyer.