Barella - Juventus-Inter - Serie A 2019/2020 - Getty Images
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The top two divisions of the Italian league, Serie A and Serie B, resumed in June following a three-month stoppage. However, all matches have been played behind closed doors since then.
"If the epidemiological curve allows, fans can return to stadiums in September," Spadafora told state broadcast Rai in a radio interview.
"Obviously, we cannot fill the stadiums as we did before, but we will have to respect a whole series of measures that are being studied at the moment."
Italy was one of the worst hit countries at the height of Europe's coronavirus pandemic and was one of the first football leagues to begin playing matches behind closed doors.
Champions Juventus are currently on course to secure a ninth consecutive Serie A title, leading the way from Atalanta by six points with three games to go.
Morning Session, Quarter-finals
Third Session, Quarter-finals
Men's Singles, Day 2
Second Session, Quarter-finals