Torriani is in line to feature for Milan in the midweek Coppa Italia tie with Lecce.
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And Il Giornale says Milan rejected an offer from Olympique Lyon over the summer for the youngster.
Milan turned down the attempt immediately, insisting Torriani is not for sale.
Last season, the young keeper made one appearance in the Champions League, one in the Coppa Italia, and six with Milan Futuro in Serie C.