Rossi then briefly battled for starting duties with Francesco Antonioli, before becoming Milan's undisputed first-choice goalkeeper, being part of a defensive line that included, amongst others, Mauro Tassotti, Franco Baresi, Alessandro Costacurta and Paolo Maldini, regarded as one of the greatest defensive units of all time. However, unlike the aforementioned defenders, Rossi wasn't selected to represent Italy in the 1994 FIFA World Cup, since former Milan coach Arrigo Sacchi, who was the commissioner of the Italian national team during this time, assigned the three goalkeeping spots to Gianluca Pagliuca, Luca Marchegiani and Luca Bucci. Under Sacchi, Rossi received two international call-ups by the end of 1994, but failed to make a single appearance for his country, although several pundits regarded him as a viable alternative to the then first-choice keeper Pagliuca; he still managed to have a successful club career under the tutelage of Fabio Capello, as the "Invincibles" went on a 58-match unbeaten run and won four "Scudetti" in five seasons, as well as the UEFA Champions League in 1994.