Several media outlets in Italy have reported the claim made by midfielder Filippo Carobbio, who was part of the Siena squad that Conte won promotion to Serie A with last season before leaving to lead Juve to the title this term.
La Gazzetta Dello Sport is one of several newspapers to quote Carobbio making the allegations, which have so far been unproven, regarding the 2-2 draw between Novara and Siena and the Tuscan side’s 1-0 loss at AlbinoLeffe late last term.
Carobbio is one of several individuals currently being investigated by prosecutors as part of the betting match-fixing probe. Conte is not one of them.
Of the Novara game, Carobbio said: "There was an agreement in place to draw the game and we discussed it during the pre-match technical meeting. We were all informed about the agreed result so that we knew how to act during the match.
"The coach, Antonio Conte, told us we needn't worry because there was an arrangement with Novara."
Regarding the AlbinoLeffe match, he added: "After Siena v AlbinoLeffe on 8 January 2011, the assistant coach Stellini asked me and Terzi to contact someone from the other team to set up an agreement for the reverse fixture later in the season, so that whoever needed the points more would be allowed to win."
Conte said back in April when the allegations first surfaced that he had no charge to answer and would relish the chance to clear his name.
"I don't have much to say," he said at the time "I've read that there’s an investigation, I'm very calm and I have faith in the institutions, who are just trying to do their jobs.
"No one has called me, but when and if they do, it will be my pleasure to see them and answer their questions.
"If anyone is looking to destabilise us, they'll find it hard to do. It will only make us more determined."
Any individual party found to be involved in match-fixing faces a potential life ban, while guilty clubs face points deductions or relegation.