However, CONI president Giovanni Malago said he could not predict whether clubs would be able to complete the season.
Serie A clubs voted on Wednesday to set June 13 as the resumption date for the league, which has been suspended since March 9, although the final decision rests with the government.
"I'd say there is a 99% chance that Serie A can resume on June 13," Malago told state broadcaster Rai, although he was less confident of getting all the remaining games played.
"To talk about the chances of it finishing, you would need a crystal ball," he said.
"It's a real risk, but Serie A's primary and only objective is to re-start."
Serie A still has 12 rounds of matches to play plus several outstanding games postponed from earlier rounds. Juventus lead the standings by one point from Lazio while Lecce, SPAL and Brescia occupy the relegation places.
Malago said the government might also change its stance on the issue of how to deal with a player testing positive -- a major sticking point so far.
The Health Ministry insists that the player's entire squad would have to go into a 14-day quarantine, which would mean matches being postponed and could play havoc with the fixture list if players at a number of teams tested positive.
The Italian football federation (FIGC) says that isolating the affected player would be sufficient providing the rest of the squad remain negative.
"I do not know the reason for the (health ministry) decision but I am told it is one that could be reviewed," Malago said.
Meanwhile, the FIGC said an inspection team would begin inspecting Serie A clubs to make sure they followed health guidelines.
"The inspection unit will verify that the training sessions of the professional clubs are carried out in accordance with the protocols which have been indicated," it said. (Writing by Brian Homewood Editing by Keith Weir)