"We are heading towards that decision," Vincenzo Spadafora told reporters when asked if the government was thinking of barring fans.
The government last month banned sporting events in the worst-affected northern regions. So far, 10 Serie A matches have been postponed as well as two in the Coppa Italia.
However, Italy's epidemic has spread, with 79 dead and 2,502 cases, and ministers are considering new measures.
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The Turin city government has called off the Juventus v AC Milan Coppa Italia semi-final second leg, which had been scheduled for Wednesday, because it could not enforce a ban on fans from affected regions.
Thursday's Napoli v Inter Milan Coppa match is also off.
Spadafora's announcement came as Serie A bosses were meeting to discuss the situation. Until now, they have preferred to postpone matches rather than play behind closed doors.
But with an already crowded fixture list, the league is running out of dates for rescheduled matches.
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